NBS SPECIAL PUBLICATION 421

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

A Guide to Methods

and Standards for the

Measurement of Water Flow
NATIONAL BUREAU OF STANDARDS

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A Guide to Methods and Standards

for the Measurement of Water Flow

Gershon Kulin and

Philip R. Compton

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Direcfor

Issued May 1975
Library of Congress Cataloging in Publication Data

Kulin, Gershon.

A Guide to Methods and Standards for the Measurement of Water Flow.

(NBS Special Publication; 421)

Includes Bibliographical references

Supt. of Docs. No.: €13.10:421

1. Flow Meters. I. Compton, Philip R., joint author. II. Title.

III. Series: United States. National Bureau of Standards. Special

Publication; 421. QC100.U57 No. 421 [TC177] 389'.08s [627'.04'2028]

75-11527

National Bureau of Standards Special Publication 421

Nat. Bur. Stand. (U.S.), Spec. Publ. 421, 97 pages (May 1975)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1975

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. C13.10:421). Price $1.65
PREFACE

Recent water pollution control legislation and the need

for a closer accounting of the disposition of our water re- sources have produced a need for more and better field measurements of water flow. Wastewater flow criteria and requirements in particular are now involving many engineers and technicians who have had little past experience in flow measurement. Getting information into the hands of those who need

and use it is one of the major thrusts of the measurements

program^ at the National Bureau of Standards. To that end

this guidebook has been compiled to provide convenient access

to useful information on good flow measurement practice and error sources for those people who have direct responsibility

for field flow measurements.

The guidebook is organized in chapters according to measuring instruments or methods. The general information sources

listed in each chapter combined with the technical references

cited at the end of each chapter are in no sense intended to

form an exhaustive bibliography on each subject. Other publications exist to fill that need.

It is intended that this document be frequently updated

and improved to increase its usefulness to readers. For that

purpose readers' comments and suggestions are invited.

iii
GUIDE TO METHODS AND STANDARDS FOR THE

MEASUREMENT OF WATER FLOW

TABLE OF CONTENTS

Page

PREFACE - iii

ABSTRACT - -- --- 1

1. INTRODUCTION - 1 1.1= Purpose 1 1.2. Scope 1 1.3. Approach 2 1.4. Evaluation of Uncertainties in Practical Measurements 2 1.4.1. General Remarks 2 1.4.2. Evaluation of Systematic Offsets in the Measurements 3

1.4.3. Random Variation 3

1.4.4. Total Uncertainty in the Measurement 3

1.4.5. Units - - 3

2. PARSHALL FLUMES - - 4

2.1. Background 4

2.2. Uses - 4

2.3. General Information Sources 4

2.4. Error Sources in Flume Use 7 2.4.1. General 7 2.4.2. The "Standard" Head-Discharge Relations 7 2.4.3. Errors in Head Measurement 7 2.4.4. Departures from "Standard" Geometry 9

2.4.5. Velocity Distribution 9 2.4.6. Other Entrance Effects 10

2.4.7. Submerged Flow - 10

2.4.8. Combined (System) Error 12

2.5. Maintenance 12

2.6. Field Calibration 12

2.7. Portable Parshall Flume - 12

2.8. References 14

3. OTHER FLUMES - 14

3.1. Introduction 14

3.2. Palmer-Bowlus Flumes 14

3.2.1. Background 14

3.2.2. General Information Sources 15

3.3. Cutthroat Flumes 15

3.3.1. Background 15

3.3.2. General Information Sources 15

3.4. Trapezoidal Flumes With Bottom Slope 18

3.5. Critical Depth Flumes 18

3.5.1. Background 18

3.5.2. General Information Sources 18

3.6. San Dimas Flume 18

3.6.1. Background 18

3.6.2. General Information Sources 18

3.7. H-Flumes --- 22

iv
Page

3.8. Errors - - - 22

3.9. References 22

4. THIN PLATE WEIRS - - - 24

4.1. Background 24

4.1.1. Rectangular Weirs 24

4.1.2. V-Notch Weirs --- - 24

4.1.3. Cipolletti (Trapezoidal) Weirs 28

4.2. Uses - 28

4.3. General Information Sources 28

4.4. Error Sources in Weir Use 31

4.4.1. General - - 31

4.4.2. The Head-Discharge Relations 31

4.4.3. Errors Due to Weir Plate Imperfections 33

4.4.4. Aeration of Suppressed Rectangular Weirs 33

4.4.5. Errors Due to Weir Slope 34

4.4.6. Upstream Velocity Distribution Effect 34

4.4.7. Supercritical Flow Channels 34

4.4.8. Errors in Head Measurement 34

4.4.9. Combined (System) Error 34

4.5. Weirs in Circular Channels 34

4.6. Maintenance 34

4.7. Field Calibration 39

4.8. References 39

5. BROAD CRESTED WEIRS - - - 39

5.1. Background ; 39

5.1.1. Square-Edge Broad-Crested Weirs 39

5.1.2. Rounded-Edge Broad-Crested Weirs 40

5.2. Uses - - - 40

5.3. General Information Sources 42

5.4. Error Sources 42

5.4.1. General --- 42

5.4.2. Head-Discharge Relations 42

5.4.3. Departures from Standard Geometry 42

5.4.4. Velocity Distribution Upstream 44

5.4.5. Errors in Head Measurement 44

5.4.6. Combined (System) Error 44

5.5. Triangular Weirs 44

5.6. Installation 44

5.7. Maintenance of Weir Structure 45

5.8. Field Calibration 45

5.9. References 45

6. PRICE AND PYGMY CURRENT METERS - 45

6.1. Background 45

6.2. Uses - - 45

6.3. General Information Sources 48

6.4. Calibration 48

6.4.1. Calibration Equations 48

6.4.2. Maintenance of Calibrations 49

6.4.3. Method of Support 49

6.4.4. Calibration Method 49

6.5. Error Sources 50

6.5.1. Meter Condition Effects 50

6.5.2. Turbulence Effects — - 50

6.5.3. Rod Not Vertical - - 50

6.5.4. Platform Motion Errors 50

6.5.5. Boundary Effects 51

6.5.6. Very Low Velocities 51

V
Page

6.5.7. Oblique Currents 51

6.5.8. Wading 51

6.6. References 51

7. PROPELLER CURRENT METERS - 51

7.1. Background 51

7.2. Uses 52

7.3. General Information Sources 52

7.4. Calibration 52

7.4.1. Calibration Equations 52

7.4.2. Maintenance of Calibrations 54

7.4.3. Method of Support 54

7.4.4. Calibration Method 54

7.5. Error Sources 54

7.5.1. Temperature 54

7.5.2. Calibration Error 55

7.5.3. Boundary Effects - - 55

7.5.4. Turbulence and Velocity Pulsation Errors 55

7.5.5. Oblique Currents 56

7.6. References 56

8. VELOCITY-AREA METHODS - 56

8.1. Background 56

8.2. General Information Sources 57

8.3. Errors in Streamgaging 57

8.3.1. Background 57

8.3.2. Numerical Example 58

8.4. Errors in Small Conduit and Sewer Measurement 59

, 8.4.1. General - - - 59

8.4.2. Numerical Example -- Rectangular Section 59

8.4.3. Numerical Example -- Circular Section 61

8.4.4. Error Due to Finite Sampling Time 61

8.5. Floats 61

8.6. Optical Current Meter - -- 62

8.7. Closed (Pressure) Conduits 62

8.8. References 62

9. CHEMICAL ADDITION METHODS - - 64

9.1. Introduction 64

9.2. General Information Sources 64

9.3. Salt Velocity Method - - 65

v.. 9.4. Dilution Methods - 65

9.4.1. Constant Rate Injection 65

9.4.2. Constant Rate Injection -- Error Sources 66

9.4.3. Length Required for Transverse Mixing 66

9.4.4. Slug Injection 66

9.4.5. Slug Injection -- Error Sources 66

9.4.6. Selection of Additives 66

9.4.7. Radioisotope Methods 68

9.4.8. Overall Accuracy 68

9.5. References 68

10. OTHER OPEN CHANNEL METHODS 69

10.1. Introduction 69

10.2. Submerged Orifice 69

10.2.1. Background - 69

10.2.2. General Information Sources 71

10.3. Free Overfall - 71

10.3.1. Background 71

10.3.2. General Information Sources 73

vi
Page

10.3.3. Error Sources and Comments 73

10.4. Acoustic Flowmeter 75

10.5. Slope-Area Method - 75

10.6. Other Methods 75

10.7. References 75

11. INSTRUMENTS AND METHODS FOR CLOSED CONDUIT FLOWS — 75

11.1. Introduction 75

11.2. Trajectory Method (Purdue) 76

11.2.1. Background - - 76

11.2.2. General Information Sources 76

11.2.3. Comments 76

11.3. California Pipe Method 76

11.3.1. Background 76

11.3.2. General Information Sources 76

11.3.3. Comments . 76

11.4. Trajectory Method (Theoretical) 78

11.4.1. Background 78

11.4.2. General Information Sources 78

11.4.3. Comments 78

11.5. Orifice at End of Pipe 78

11.6. Elbow Meters --- --- - 80

11.6.1. Background 80

11.6.2. General Information Sources 80

11.7. Segmental Orifices 80

11.7.1. Background 80

11.7.2. General Information Sources 80

11.8. Orifice Meters --- 80

11.8.1. Background - 80

11.8.2. General Information Sources 82

11.8.3. Errors - 82

11.9. Nozzle Meters - 82

11.10. Venturi Meters 82

11.10.1. Background 82

11.10.2. General Information Sources 82

11.10.3. Errors --- - 83

11.11. Magnetic Flowmeters 83

11.11.1. Background - 83

11.11.2. General Information Sources 83

11.12. Acoustic Flowmeters 83

11.12.1. Background 83

11.12.2. General Information Sources 85

11.12.3. Comments --- 85

11.13. Chemical Addition Methods 85

11.14. Velocity-Area Methods 85

11.15. References 85

APPENDIX A -- Conversion to SI Units 86

APPENDIX B -- Definition of Terms - 86

vii

GUIDE TO METHODS AND STANDARDS FOR THE

MEASUREMENT OF WATER FLOW

Gershon Kulin and Philip R. Compton

Selected information sources on methods and standards for

making measurements of water and wastewater flow in the' field

are listed and described. Both closed conduit and free surface

flows are treated, but emphasis is on open channel flow measurements needed in water resource engineering and in water pollution control. Instruments and methods covered include weirs,

flumes, current meters (and velocity traverse methods), dilution

techniques, pipe flow instruments, acoustic meters and others.

In addition to summarizing the basic properties of each instrument or method and referring users to the best available sources

of detailed information on performance and field application,

potential sources of error are described and quantified where

possible

.

Key words: Flow measurement, water; instruments, flow measurement; open channel flow measurement; pipe flow measurement;

standards, flow measurement.

1 . INTRODUCTION

Population density and advanced technology continue to place increasing demands upon

the nation to conserve its supply of water and to control the quality of its water.

Recent legislation and a heightened public interest in conservation and environmental

matters have emphasized the importance of water velocity and flowrate measurements conducted

in the field. Uniform and reliable measurement data are needed in order to identify the resource levels and quality of bodies of water; determine the results of conservation and

quality control efforts; and enforce water conservation and quality regulatory requirements .

1.1. Purpose

The information presented in this guidebook is intended to assist measurement

supervisors and their personnel engaged in establishing and operating water and wastewater flow measurement stations in the field. It is geared to technical people who are not necessarily fluid mechanics specialists.

Several good flow measurement handbooks are now available, including the Bureau of

Reclamation's Water Measurement Manual and the U. S. Geological Survey series on Techniques of Water Resources Investigations. However, no single source provides all of the

information needed by workers in the field, and the major purpose of this guidebook is to

identify and describe the most useful sources in one document. Also, flow measurement

references frequently do not point out potential errors and pitfalls nor attempt to

quantify them. It is expected that the comments given here will prove useful to readers

in that regard.

1.2. Scope

Information on flow measurements in pressure conduits as well as in open channels is

included in this publication. However, the open channel measurements have been emphasized for two reasons. First, information on the traditional pipe flow measuring instruments, e.g., orifice and venturi meters, generally appears to be more widely available in

popular sources than corresponding open channel information; and second, free surface flows are so frequently encountered in water pollution and water resource flow measurement.

Within the context of open channel measurements, the traditional instruments and methods

1
have been emphasized rather than newer, more sophisticated devices, because the majority of users will have only the traditional means available to work with, at least in the near

future

.

Although the information provided herein will be useful for many water flow applications, some emphasis has been given to problems peculiar to wastewater measurements.

The reason is that recent legislation in this field is bringing about the involvement of

many workers who are relative newcomers to flow measurement activity.

1.3. Approach

Each instrument or method is introduced with a brief description of its operation or utilization. In some cases this description contains what appears to be all the information needed to make measurements. For example, it is difficult to describe thin-plate

weirs without listing some of the "standard" equations and geometries in use. Nevertheless, this document is intended not as a self-contained measurement manual but as a guidebook to sources of detailed information. Good measurements (or, if "good" measurements

are impossible, an appreciation of the errors involved in the best possible measurements

under the circumstances) depend upon attention to published detail, appreciation for the

subtleties of the flow and measurement process and the experience of others.

The general information sources listed in each section of this guidebook are intended to provide these details. The references at the end of each chapter, on the other

hand, provide technical backup material which, although useful, is not necessarily of as much immediate importance to the user as that contained in the general information sources.

The compilers of this guidebook have tried to provide enough ordering information to

make the general information sources as accessible as possible. We have assumed that most

field users will not have rapid or convenient access to a large technical library. No

foreign language sources are used, and no foreign English- language general information

sources are cited unless they can be conveniently obtained from domestic sources without

undue delay.

1.4. Evaluation of the Uncertainties in Practical Measurements

Section 1.4 has been contributed by J. M. Cameron, Chief, Office of Measurement Services, Institute for Basic Standards, National Bureau of Standards.

1.4.1. General Remarks

A flow measuring device, once installed, will be called upon to make a sequence of

measurements throughout its useful life. It is the measurements in this sequence for which

one needs assurance that errors are suitably small. What is needed is not merely a description of the properties of the instrument, but rather of the measurement process generated by that instrument. The properties of this process will depend on many factors in addition to the instrument - errors in installation, properties of the fluid involved, in some cases on operator technique, etc. One also needs continuing evidence that the process

is "in control."

These questions could easily be answered if one had a much more accurate measuring

method available and could periodically check the measurements. One could study the differences between the two methods and make statements about the offset of one relative to

the other and describe the distribution of the observations about that offset point. The

size of the systematic offset and the scatter of the values might turn out to be a function of flow rate, contaminants in the fluid, and a host of other factors. However, the

ability to "sample" the output enables one to arrive at whatever degree of knowledge of the

process is needed or is economically feasible.

Next best would be the presence of redundancy in the form of a second instrunsnt, but

most often one has to rely on indirect evidence such as that given by the day-to-day con- sistency of the flow being measured. In this latter case one might be satisfied with his

knowledge of the performance of the device with respect to random variations but one does

not have any direct measure of the offset due to systematic errors in the system. One

2
therefore desires to set bounds to the possible extent of these systematic effects as well

as having an error limit for those statistical variations that appear to be random in

nature

1.4.2. Evaluation of Systematic Offsets in the Measurements

For each measurement method a number of possible sources of systematic error can be

listed. These fall into several general classes such as: (a) those related to departures

from ideal geometry or correct installation; (b) those related to the approximating equation or calibration used; (c) those related to the velocity and flow characteristics of the

fluid; (d) those related to impurities and contamination in the fluid; and (e) those re- lated to wear, aging or other changes in instrument response.

The ideal method of setting bounds for the possible bias remaining after known cor- rections for the factor have been made, is that of measuring the deviation resulting from

introducing a change corresponding to the maximum expected in practice. For example, the

geometry can be varied, the properties of the liquid changed or procedural changes introduced as a part of the regular measurement. The resultant changes constitute bounds to the

effect from the source being varied.

In many cases one knows only that a certain parameter is correct to within some percentage value. Often one can compute the effect such an uncertainty will have on the

results. This sort of bound is of unknown quality because the formula by which it is com- puted does not take account of all the possible effects of the variable involved.

One has the problem of how to combine the various limits of error. Unless one has

experiment or theory to determine the effect of joint variation of two or more factors,

the correct method of combination will not be known. Until the bounds can be verified by

experiment, arguments over whether a sum of absolute values or a root sum of squares is

better cannot be settled. One should list all error bounds and the rule of combination

used to arrive at the bound to be used for the limit to the offset or systematic error of

measurements made by the process.

1.4.3. Random Variation

Even if one could reproduce the same flow again and again it is characteristic of mea- surement processes that they would not give the same results. The random variation so ex- hibited is a characteristic of the instrument and flow condition and may depend on rate,

fluid involved, etc. An umpire method, or a second instrument enables one to estimate this

random variation directly. However in most cases one cannot reproduce the flow exactly so that the random variation includes a component from variations in the flow itself.

For a proper characterization of instrument performance one needs a bound for the'effect of all the components of random error in the process. This variation is usually ex- pressed by a standard deviation which can be associated with the values from the instrument, and the limit is taken to be three (some people use two) times this standard deviation.

1.4.4. Total Uncertainty in the Measurement

A single value reported out by the process will be uncertain by an amount that depends on the sum of the systematic offset and the random error which occurs. The average

of several measurements will reduce the effect of the random errors by a factor depending

on the square root of the number of measurements, but the systematic error in the average

will not be reduced at all. For this reason, one should state both elements of the total

uncertainty and report the sum as the possible uncertainty.

1.4.5. Units

Conventional units have been used throughout this publication, mainly because these ar still the units most often used by those concerned with water and wastewater flow measurements. However, because of the increasing importance of International Standard (SI) units,

the factors for conversion from conventional to SI units are listed in Appendix A for

3
those units used in this document.

2. PARSHALL FLUMES

2.1. Background

The Parshall flume was developed in the late 1920's primarily to measure irrigation

water but it is now frequently used in sewers and sewage treatment plants as well. The

flume shape and standard sizes are shown in figure 2.1. Although it is operable with the

crest overfall either free or submerged*, it is highly desirable to select and place the

flume so that the overfall is free. The reason is that in free flow the flowrate can be

deduced from a single upstream depth measurement, while in submerged flow the downstream

depth has to be obtained also.

The head-discharge equations for free flow are of the form

Q = CH^ [2.1]

where Q is the discharge in cubic feet per second and H is the depth in feet measured at

the location "a" in figure 2.1. Values of C and n are given in table 2.1. The free flow

discharges computed from eq. 2.1 and table 2.1 can be found in tabular or graphical form

in many of the references cited in this chapter.

The flow becomes submerged when the downstream depth (measured at "b" in figure 2.1)

attains a certain critical percentage of the upstream depth as given in table 2.2. In the

1, 2 and 3 inch flumes it has been found that a more reliable downstream head measurement

can be made at "c" (see figure 2.1) than at "b." The relationship between H and H, is

given in a curve in re f. 2.3.1.

Curves for submerged flow , for which eq. 2.1 and table 2.1 are not valid, are available in refs. 2.3.1, 2.3.2, 2.3.4 and 2.3.5. Reference 2.3.3 has submerged flow curves

for small flumes only. The effect of submergence on the discharge is shown approximately

in figure 2.2. Actually the percentage flow reduction varies slightly over the discharge

range for each- flume size. (See also section 2.4.7.) Figure 2.2 is included mainly to

give users an idea of submergence effects; to achieve accuracy the more detailed submerged flow curves in the general information sources of section 2.3 should be consulted.

2.2 Uses

The principal advantages of the Parshall flume are its capability for self -cleansing

(particularly when compared with sharp-edged weirs) and its relatively low head loss.

These characteristics of the Parshall flume make it particularly suitable for flow measurement in irrigation canals, in certain natural channels, and in sewers. An important disadvantage is that it is not amenable to theoretical treatment, so that the dimensions of

figure 2.1 must be closely adhered to if the empirical information of table 2.1 is to be

valid. See also section 2.4.4.

2.3. General Information Sources

2.3.1. "Water Measurement Manual," Bureau of Reclamation, U. S. Dept. Interior, Second Ed.,

Revised Reprint, 1974, Ch. 3, pp. 43-88. Order from U. S. Govt. Printing Office,

Washington, D. C. 20402. $5.80. Cat. No. 127 . 19/2 : W29/2 , Stock No. S/N 2403-0027.

This chapter is a fairly comprehensive treatment of the Parshall flume and is

particularly strong on flume selection and placement to avoid submergence.

Head loss data is also given.

2.3.2. "Measurement of Irrigation Water," Section 15, Chap. 9 of National Engineering

Handbook . U. S. Dept. Agriculture, Soil Conservation Service, 1952. Order from

*See Appendix for definition of terms.

4
w A B c

1 D E T G H K M N ]P R X Y z

FT. IN, FT IN FT IN FT IN FT IN. FT IN FT IN FT IN FT IN FT IN FT IN FT IN. FT IN. FT IN FT IN FT IN. FT IN. FT IN.

1

1^

2^

3^

1

1

1

7^

6|

1

1

101

4

1

1

2

4

6

0 3i

5,^7

0

io,i

0

Ito

l'/2

6 to 96 to 10

0 3

4i

6

0

1

8

100

0

1

85

10^

532

0

34

7e

1

0 I5

2i

1 -

_

0

5

16

5

e

1

0 2

1

0

1e

1 4

2 0 6 2

7

16 -p

4| 2 0 1 3i 1 3| 2 0 1 0 2 0 0 3 1

i 0 0 4i 1 1 2 4 0 2 0 3 9 2 lOf 1 Hi 2 10 1 3 1 I0| 2 6 1 0 1 6 3 0 4^ 3 6i 4 2 3

1 0 4 6 3 0 4 2 0 2 9i 3 0 2 0 3 0 3 3 9 4 10^ 8 2 3

1 6 4 9 3 2 4 n 2 6 3 4| 3 0 2 0 3 0 3 3 9 6 8 2 3

2 0 5 0 3 4 4 101 3 0 3 14 3 0 2 0 3 0 3 3 9 6 1 8 2 3

3 0 5 6 3 8 5 4i 4 0 5 11 3 0 2 0 3 0 3 3 9 7 3^ 8 2 3

4 0 6 0 4 0 5 lOf 5 0 6 4i 3 0 2 0 3 0 3 6 9 8 I0| 2 0 2 3

5 0 6 6 4 4 6 4^ 6 0 7 6f 3 0 2 0 3 0 3 6 9 10 li 2 0 2 3

6 0 7 0 4 8 6 io| 7 0 8 9 3 0 2 0 3 0 3 6 9 1 1 3i 2 0 2 3

7 0 7 6 7 4j 8 0 9 III 3 0 2 0 3 0 3 6 9 12 6 2 0 2 3

8 0 8 0 5 4 7 9 0 1

l| 3 0 2 0 3 0 3 6 9 13 8i 2 0 2 3

10 0 6 0 14 0 12 0 15 7i 4 0 3 0 6 0 0 5 1 ly 0 0 9

12 0 6 8 16 0 14 8 18 4| 5 0 3 0 8 0 6 1 I5 0 9

15 0 7 8 25 0 18 4 25 0 6 0 4 0 10 0 9 1 6 0 9 20 0 9 4 25 0 24 0 30 0 7 0 6 0 12 0 0 2 3 0 9

25 0 1 1 0 25 0 29 4 35 0 7 0 6 0 13 0 0 2 3 0 9

30 0 12 8 26 0 34 8 40 4| 7 0 6 0 14 0 0 2 3 0 9 40 0 16 0 27 0 45 4 50 9^ 7 0 6 0 16 0 0 2 3 0 9 50 0 19 4 27 0 56 8 60 9^ 7 0 6 0 20 0 0 2 3 ,0 9

'

Figure 2.1. Parshall flume dimensions, from ref. 2.3.1.

5
Table 2. 1

Free Flow Values of C and n for Parshall Flumes

(See Equation 2.1)

Flume Throat, W C n Max. Q, cfs

1 in 0.338 1.55 0.2

2 in 0.676 1.55 0.5

3 in 0.992 1.55 1.1

6 in 2.06 1.58 3.9

9 in 3.07 1 53

0 026

1.522W^'"^''

8.9

1 ft 4W (*) 16.1

1.5 ft II II 24.6

2 ft II II 33.1

3 ft II II 50.4

4 ft It II 67.9

5 ft II II 85.6

6 ft II II 103.5

7 ft II II 121.4

8 ft II II 139.5

10 ft 39.38 1.6 200

12 ft 46.75 1.6 350

15 ft 57.81 1.6 600

20 ft 76.25 1.6 1000

25 ft 94,69 1.6 1200

30 ft 113.13 1.6 1500

40 ft 150.00 1.6 2000

50 ft 186.88 1.6 3000

(*) W in feet

U. S. Govt. Printing Office, Wash., D. C. 20402. $1.10. Cat. No. A57 . 6/2 : En3/sec

15, Ch. 9, S/N 0107-00708.

The section of this document dealing with Parshall flumes covers roughly the same material as ref. 2.3.1 above.

2.3.3. ASTM Standard D1941-67, "Standard Method for Open Channel Flow Measurement of

Industrial Water and Industrial Waste Water by the Parshall Flume." Order from

American Society for Testing and Materials, 1916 Race St., Philadelphia, Pa.

19103. $1.50.

This standard gives a brief treatment of the Parshall flume. Useful details

on stilling well design for head measurement are included. Information is

given only on flumes up to 8 ft in throat width.

2.3.4. "Design and Calibration of Submerged Open Channel Flow Measurement Structures,

Part 2 -- Parshall Flumes," G. V. Skogerboe, M. L. Hyatt, J. D. England and J. R. Johnson, Rep. No. WG31-3, Utah Water Research Lab., 1967. Order from Utah Water

Res. Lab., Utah State Univ., Logan, Utah 84321. $0.25.

This report has details on flume use under submerged flow.

2.3.5. "Stevens Water Resources Data Book," First Edition, Leupold & Stevens, Incorporated, P. 0. Box 688, Beaverton, Ore. 97005. $4.00.

This source is particularly useful for evaluating error sources in head

6
measurements for flumes and weirs using float actuated gages. Errors related

to internal friction, float size, humidity effects on chart paper, etc., are covered.

2.3.6. Davis, S., "Unification of Parshall Flume Data," Proc. Amer. Soc. Civ. Eng., 87 , IR4, Dec. 1961, pp. 13-26. Order from Engineering Societies Library, 345 E. 47th

St., New York, N. Y. 10017. $0.25 per page plus $3.00.

2.3.7. In addition to the sources cited above, several other well-known hydraulic source

books, e.g., reference 2.8.1, list the "standard" flume dimensions and give the

head-discharge relations of section 2.1 above in either tabular or graphical form.

The original sources of virtually all of the data are the publications of Parshall

(2.8.2, 3, 4) with data on the smallest flumes added by Robinson (2.8.5).

2.4. Error Sources in Flume Use

2.4.1. General

As is true for all flow measuring devices, the accuracy of the result depends upon the

performance of the instrument treated as a system -- in this case (a) the primary element

(flume), (b) the secondary element (depth sensor and recorder), and finally (c) the manner

in which these elements are installed and maintained. The following sections deal with

these three aspects.

2.4.2. The "Standard" Head-Discharge Relations

The published head-discharge relations which are given in section 2.1 above and in sources such as refs. 2.3.1, 2, 3, 4 are apparently all based on the original experiments

of Parshall (2.8.2, 3, 4). However, there might be uncertainties in these relations of up

to 5 percent; this is recognized by the ASTM standard (2.3.3). For example, extensive

data by Blaisdell (2.8.6) indicate differences of up to 6 percent from the "standard"

relations. It is therefore imperative that flumes be calibrated in place if accuracy of

the order of 2 percent in the head-discharge relation is desired.

2.4.3. Errors in Head Measurement

From eq. 1.1 and table 2.1 it is seen that the percentage error in head measurement is

multiplied by approximately 1.5 (the value of n) to determine its contribution to the percentage error in flowrate. Accurate head measurements are therefore particularly important to the overall accuracy of flow rates determined with flumes and weirs.

Some etrors associated with operation of float actuated gages and recorders are treated in ref. 2.3.5. As an illustration to alert users to the potential for these

errors, a system with a 6-inch diameter float and requiring a 2-ounce force to move it can have a float-lag error as high as 0.02 ft of head. At low heads this error is significant.

For example, the flowrate error in a flume operating at a head of 0.5 ft would be about 6 percent. Errors from this source can be reduced by using larger floats and by minimizing

internal friction. No error information on scow float performance is available.

Small systematic errors in head measurement caused by failure to accurately reference

the gage zero to the crest elevation can be similarly damaging to accuracy. See also com- ments on level in section 2.4.4.

The foregoing errors in head measurements do not include all of the systematic and

random errors which could actually occur on site. See Introduction and section 2.4.8 for

further comments on this subject.

7
100

50 I \ \ \ \ 1 50 60 70 80 90 100

Submergence, H^^/H, in percent

Figure 2.2. Approximate submergence effect on Parshall flume

discharge, from ref. 2.3.1.

Figure 2.3. Potential hydraulic jump development in a Parshall

flume

8
2.4.4. Departures from "Standard" Geometry

If the standard head-discharge relations are to be used, the standard flume dimensions must be strictly adhered to. For the smallest flume sizes, tolerances of 1/64 inch

have been suggested for the throat, with 1/32 inch tolerance elsewhere (2.3.1). In a 1-inch flume a throat width difference of even 1/64 inch will cause a 1.5 percent error unless corrected for as in the following paragraph.

Width. If the throat width differs slightly from the standard dimension, it has been

recommended (2.3.1) that the standard flowrate be changed proportionately, e.g., if the

throat of a 1 ft flume is 1/8" too narrow, the flowrates in the standard tables should be

reduced by 1 percent at each value of H. This correction should be applied with discretion, because there are no guidelines yet as to how large the departure from the standard

throat dimension can be before this correction procedure becomes invalid. Probably it

should be restricted to throat width changes of a few percent only.

No guidelines presently exist for adjusting the discharge when the width at the mea- suring section differs from the recommended width. Accuracy of this dimension is usually

not as critical as that of the throat width.

For flumes which are not of standard dimensions but which have the correct sidewall

convergence angle, and for flumes in which only the location of the depth measurement is

incorrect, corrections can be made by the method of Davis (2.3.6).

Level . No guidelines exist for adjustment of head-discharge curves of flumes which

are not level longitudinally. If the flume is slightly out of level transversely, we can only use the standard H-Q curves provided an average H is used. Caution : A staff gage

mounted on the flume sidewall at the measuring station will give an incorrect head reading

if the flume tilts laterally, with the direction of the error depending on whether the

gage is mounted on the "deep" or "shallow" side.

Length . The converging section of the flume (length B in figure 2.1) cannot be

shortened without affecting the performance (2.8.7). There is no discernible effect if it

is lengthened, but the head-measuring station should remain at the standard distance from

the brink. There is reportedly no difference in performance between the curved and

straight entrance wingwalls of figure 2.1. However, the curved entrance appears to in- sure smooth flow at the head-measuring station.

2.4.5. Velocity Distribution

The entrance transitions and converging sidewalls of the Parshall flume provide a small favorable pressure gradient which tends to straighten the velocity distribution.

However, this gradient is too small to adjust grossly distorted velocity profiles in the

approach flow and if these are permitted to exist, the flume will not produce the standard performance (2.3.1). Therefore situations which distort the entering flow should be

avoided. Examples are:

Placement of flume immediately downstream of a bend, junction or turnout without

allowing sufficient flow straightening length.

Discharging from a narrower conduit into a wider flume entrance without providing

enough entrance length for the flow to become evenly distributed across the section. Construction of a transition section (see, e.g., ref. 2.8.1) can be helpful here if available length is restricted.

Comparatively small changes in velocity distribution, such as those associated with

change in roughness of an artificial channel, probably do not affect measurements significantly, at least in small flumes. However, more research is needed on this subject to

provide a basis for a more definitive statement.

The velocity distribution is usually expressed in terms of a velocity distribution

coefficient, a, (see Appendix) which would have a value of unity for a completely uniform distribution. For turbulent flow in relatively smooth channels, Oi is close to unity.

9
typically around 1.05. Typical values for various field situations can be found in other

references, such as 2.8.1.

In the absence of substantial experimental evidence on the ability of the Parshall

flumes to flatten nonuniform velocity distributions, it is best to avoid high values of a

by providing a long and regular entrance channel where possible. Unfortunately no published recommendations on minimum lengths are available. Pending further research, only

in-place calibrations can inspire confidence in H-Q curves where conditions are such that

distorted velocity distributions are expected in the approach flow.

2.4.6. Other Entrance Effects

Supercritical Flow . The Parshall flume should not be placed at a lower elevation than

that of the channel being measured, because of the danger of inducing supercritical flow

and a hydraulic jump within the flume. See figure 2.3. One flume so installed, in which

a diagonal jump formed near the float gage, was found to be under-registering by amounts

up to 40 percent at low flows.

When the channel is steep and flow is always supercritical, a check should be made

using hydraulic jump principles (see, e.g., ref. 2.8.1) to insure that the jump occurs sufficiently far upstream of the flume to permit smoothing of the flow. Reference 2.8.8 rec- ommends a minimum distance of 20 channel widths upstream.

Weak hydraulic jumps with upstream Froude numbers between 1,2 and 1.7 should in particular be avoided near the flume. These jumps are characterized by long- lasting standing

waves downstream and the flume depth measurement will be erroneous. Stilling wells cannot

average out the depths associated with stationary waves.

2.4.7. Submerged Flow

It is highly desirable that flumes be installed so that they operate in free flow.

The ratio between downstream depth, H^, (see figure 2.1) to upstream depth H, at which

submergence begins to affect the upstream conditions is given in table 2.2 below for the

various flume sizes.

Table 2.2

Critical Submergence for Parshall Flumes

(Data from Ref. 2.3.4)

Flume Size Critical Submergence Flume Size Critical Submergence

1 in 0.56 3 ft 0.68

2 in 0.61 4 ft 0.70

3 in 0.64 5 ft 0.72

6 in 0.55 6 ft 0.74

9 in 0.63 7 ft 0.76

1.5 ft 0.64 10 to 50 ft 0.80

2 ft 0.66

Even submergence ratios slightly in excess of the critical ratios of table 2.2 can introduce significant errors if they are not taken into account by use of submergence

curves in, e.g., ref. 2.3.1. This is shown in figure 2.4 for a 1 ft flume where errors

as large as 10 percent occur at low heads for uncorrected submergence of 70 percent. Even

at the higher flows the error exceeds 3 percent for 70 percent submergence. At high submergence the error becomes intolerable for most applications.

10
11
Even when the submergence correction is properly made, a small error can be introduced, particularly at large submergence, if the depth measurements are in error. Consider a 1-ft flume with H = 1.00 ft and = 0.85 ft, so that the nominal submergence is 85

percent. But if each of the two depth measurements is uncertain by as much as + 1 percent,

then the actual submergence ratio could be (although it is not likely to be) as high as 86.7 percent or as low as 83.3 percent. From figure 2.2 or the curves of, e.g., ref.

2.3.1, this corresponds to a discharge spread of 5 percent. This example (in which any

uncertainty in the correction curves themselves has been ignored for lack of information)

illustrates the desirability of designing flume installations for free flow.

2.4.8. Combined (System) Error

The foregoing discussions of error sources can help the user to estimate some, but not

all, of the error components which contribute to the total error of measurement. Other

errors, particularly those relating to installation, maintenance, aging and wear, cannot be

estimated without some sort of In place check on the performance, as described in the Introduction. Nevertheless, in selecting or evaluating a new system that is to be, or has

been, installed in accordance with good practice, the user can still try to make a useful

estimate of the total system error in advance of installation or of in-place rating. However, it is important to recognize the limitations of such an estimate.

As an illustrative example, consider a 1-ft Parshall flume that is constructed and

installed according to recommended practices. Taking into account the discussion of errors in section 2.4.2, the user might still want to assign a possible error of, say,

3 percent to the flowrates published in the Parshall flume tables. The user can also

estimate how closely he was able to reference the head zero to the crest elevation. Suppose for the sake of illustration that this referencing is within 0.02 ft; how this will

change with use cannot be estimated. Suppose also that from information in ref. 2.3.5 or other sources, the user estimates the head measuring instrument to be accurate within 0.01

ft; again the effects of use on this figure cannot be estimated in advance.

One way of computing a combined estimated error from the foregoing components is by

the square root of the sum of the squares, so that in view of eq. 2.1

H = 2.0 ft: Error = [ (0.03) + (1.522)2[ (0.01)2 = (0.005)2]^% = 3.4 percent

H = 0.5 ft: Error = [ (0.03)2 + (l.522)2[ (0.04)2 + (0.02)2]]^ = 7.4 percent

Again, the above illustrative results include only those sources of systemmatic error

that can be reasonably estimated for conditions at the outset. Systemmatic errors that develop in place and random errors cannot be accounted for in this way.

2.5. Maintenance

Although the Parshall flume was originally developed to pass moderate sediment loads,

heavy debris is known to settle out and affect the performance of the meter. Periodic

cleanouts are therefore recommended for sewage meters. Periodic calibrations of float

gage, scow float and recorder are needed, as well as checks on flume level.

2.6. Field Calibration

1. By current meter traverse, see Chapter 8.

2. By dilution methods, see Chapter 9.

3. By thin plate weir, see Chapter 4.

2.7. Portable Parshall Flume

A portable modified Parshall flume has been developed by the U. S. Geological Survey

(2.8.9) in the 3-inch size. Figure 2.5 shows this flume and its rating table. It is

intended for free flow only, so it has no diverging section. The converging section is

shorter and the angle of convergence slightly larger than in the standard 3-inch flume.

The discharge is higher than in the standard flume for each measured head.

12
13
2.8. References

2.8.1. Chow, V. T., "Open Channel Hydraulics," McGraw-Hill, 1959, pp. 75-81.

2.8.2. Parshall, R. L., "Parshall Flumes of Large Size," Colorado Agricultural College

Bull. 386, May 1932.

2.8.3. Parshall, R. L. , "The Improved Venturi Flume," Colorado Agricultural College

Bull. 336, March 1928.

2.8.4. Parshall, R. L. , "The Parshall Measuring Flume," Colorado State College Bull. 423,

March 1936.

2.8.5. Robinson, A. R. , "Parshall Measuring Flumes of Small Sizes," Colorado State Univ.,

Tech. Bull. 61, 1957.

2.8.6. Blaisdell, F. W. , "Discussion of Model-Prototype Conformity," Trans. ASCE, 109 , 1944, pp. 1944, pp. 157-167.

2.8.7. Hauser, V. L. , "Relation Between the Flowrate Equation and Length of Converging

Section of Parshall Flume," Trans. ASCE, 1960, pp. 86-88.

2.8.8. British Standards Institution, Standard No. 3680-4A, "Methods of Measurement of

Liquid Flow in Open Channels, Part 4A: Thin Plate Weirs and Venturi Flumes,"

1965.

2.8.9. Buchanan, T. J. and Somers, W. P., "Discharge Measurements at Gaging Stations,"

Chapter A8, Book 3 of Techniques of Water-Resources Investigations of the United

States Geological Survey , 1969.

3. OTHER FLUMES

3.1. Introduction

Although Parshall flumes are the most frequently encountered flumes in water delivery

and wastewater systems today, there are other types of flumes which are in use and warrant

discussion. Also, there are flumes which have been developed only recently and which are likely to be used frequently in the future.

In the following, each flume is briefly described and selected information sources

are cited. Proprietary flumes are not included.

3.2. Palmer-Bowlus Flumes

3.2.1. Background

Palmer-Bowlus flumes are formed by placing inserts into canals and sewers which raise

the bottom and/or constrict the sidewalls. See figure 3.1 for a typical example.

Many Palmer-Bowlus flumes are in use in the United States. Their principal advantage lies in simplicity of construction and ease of installation through manholes. Also,

because critical and nearly parallel flow is attained in the throat section, the flume is

amenable to analytical treatment using critical flow principles. According to the experiments of Wells and Gotaas (3.2.2.1), performance of Palmer-Bowlus flumes inserted into

U-shaped channels can be predicted theoretically within 3 percent, so long as the upstream

depth does not exceed 0.9D, where D is the diameter of the circular conduit leading into

U-channel. Users are cautioned that there appear to be no other published data on this

flume to corroborate this conclusion.

14
3.2.2. General Information Sources

3.2.2.1. Wells, E. A. and Gotaas, H. B., "Design of Venturi Flumes in Circular Conduits,"

Amer. Soc. Civ. Eng., 82_, Proc. Paper 928, April 1956, 23 pp. Order from Engineering Societies Library, 345 E. 47th St., New York 10017. $0.25 per page plus

$3.00.

This paper gives the theoretical basis for the Palmer-Bowlus flume and com- pares theoretical predictions with the results of numerous laboratory ex- periments on various flume shapes, i.e., bottom-sidewall insert combinations. Limitations on its use are described based on the specific energy

of the approach flow.

3.3. Cutthroat Flumes

3.3.1. Background

The cutthroat flume derives its name from the absence of a parallel-wall throat section.

See figure 3.2. It is a flat-bottomed device whose main advantage is extreme simplicity of

form and construction. The general form of the discharge equation for free flow is

Q = KW^-°"h "1 = Ch "1 [3.1]

where W is the throat width, h is the upstream depth measured at the location shown in

figure 3.2, n^ is the free-flow exponent, and C and K are free-flow coefficients. Free

flow values needed for eq. 3.1 are given in Table 3.1 for a family of flume dimensions.

Since K and n^ depend only on flume length, interpolations can be made for coefficients of

intermediate size flumes which are proportioned according to figure 3.2.

The discharge equation for submerged flow is of the form

Q = C^(h^ - log S)""^ [3.2]

where h^ is the downstream depth measured as in figure 3.2, submergence S is h^/h , n2 is

the submerged- flow exponent, and C, = Kj^wl''^25^ Table 3,1 lists the values needei for use

in eq. 3.2 as obtained experimentally for a family of flumes. Again interpolation for

intermediate flume sizes is possible.

Note: There are no experimental data published to compare with the empirical eqs.

3.1 and 3.2, so no evaluation of their accuracy can be made here. The developer recommends (for increased precision) that throat-width to flume-length ratios between 0.1 and

0.4 be used.

A major error source can occur in all flumes installed in earth channels if there is

downstream scour and the flume thereby acquires a downward longitudinal slope. The cutthroat flume is the only one for which some data exist on the effect of such slopes

(3.3.2.3). These results are reproduced in table 3.2 for free flow only. Submerged flow

data are available in ref. 3.3.2.3.

Reference 3.9.1 discusses the cutthroat flume from the viewpoint of its use in sewage

treatment plants. For example, selection of a flume for installation immediately downstream of a grit chamber is covered.

3.3.2. General Information Sources

3.3.2.1. Skogerboe, G. V., Bennett, R. S., and Walker, W. R. , "Generalized Discharge

Relations for Cutthroat Flumes," Proc. Amer. Soc. Civ. Eng., 98, IR4, Dec. 1972,

569-583. Order from Engineering Societies Library, 345 E. 47th St., New York,

N. Y, 10017. $0.25 per page plus $3.00.

This paper gives analytical and experimental background for table 3.1.

15
0.1 D

L-D/2-J ~r \ ' Point of depth meas A - A

Figure 3.1. Example of a Palmer-Bowlus flume,

16
3.3.2.2. Skogerboe, G. V., Hyatt, M. L. , Anderson, R. K. , and Eggleston, K. 0., "Design

and Calibration of Submerged Open Channel Flow Measurement Structures, Part 3 -- Cutthroat Flumes," Utah Water Research Lab. Rep. WG31-4, 1967. Obtain from Utah

Water Research Lab., Utah State Univ., Logan, Utah 84321, $0„25.

Table 3.1

Coefficients and Exponents for Cutthroat Flumes

(See Eqs . 3.1 and 3.2)

Length, L Width, W Free Flow Submer ged Flow

ft ft C

1 K C,

1 ^"2

9.00 1.000 3.50 1.560 3.500 1.688 1.390 1.700

9.00 2,000 7.11 1.560 3.500 3.430 1.390 1.700

9.00 4.000 14.49 1 . 560 3. 500 6. 970 1.390 1.700

9.00 6.000 22.0 1 . 560 3.500 10.600 1.390 1.700

4.50 0.250 0.96 1.720 3.980 0.548 1.410 2.250

4.50 0.500 1.96 1.720 3.980 1.120 1.410 2.250

4.50 1.000 3.98 1.720 3.980 2.275 1.410 2.250

4.50 2.000 8.01 1.720 3.980 4.575 1.410 2.250

3.00 0.167 0.719 1.840 4.500 0.413 1.480 2.580

3.00 0.333 1.459 1.840 4.500 0.837 1.480 2.580

3.00 0.667 2.970 1.840 4.500 1.705 1.480 2.580

3.00 1.333 6.040 1.840 4.500 3.465 1.480 2.580

1.50 0.083 0.494 2. 150 6.100 0.261 1.741 3.250

1.50 0.167 0.974 2.150 6.100 0.516 1.741 3.250

1.50 0,333 1.975 2.150 6. 100 1.048 1.741 3.250

1.50 0.667 4.030 2.150 6.100 2.140 1.741 3.250

Table 3.2

Effect of Floor Slope on Cutthroat Flumes

(See Equation 3.1)

^ength, L Width, W Floor Slope Free Flow

ft ft ft/ft C ^

1.50 0.167 0.0000 0.974 2.150

1.50 0.167 0.0278 1.075 2.150

1.50 0.167 0.0556 1.220 2.150

1.50 0.167 0.0833 1.390 2.150

1.50 0.333 0.0000 1.975 2. 150

1,50 0.333 0.0278 2. 180 2.150

1.50 0.333 0.0556 2.470 2.150

1.50 0.333 0.0972 2.990 2.150

4.50 0.500 0.0000 1.960 1.720

4.50 0.500 0.0185 1.980 1.720

4.50 0.500 0.0556 2.140 1.720

4.50 0.500 0.1078 2.560 1.720

4.50 1.000 0.0000 3.980 1,720

4.50 1.000 0.0185 4.000 1.720

4.50 1.000 0.0556 4.350 1.720

4.50 1.000 0.1064 5.200 1.720

17
This report discusses only one size of the rectangular cutthroat flume, the

results of which are already included in ref. 3.3.2.1. However, data on cutthroat flumes of trapezoidal and triangular section are also included in this

report

.

3.3.2.3 Skogerboe, G. V., Walker, W. R. , Wu, T-Y, and Bennett, R. S., "Slope-Discharge

Ratings for Cutthroat Flumes," Trans. Amer. Soc. Agric. Eng., _16, 1, 1973,

78-81. Copy available from American Society of Agricultural Engineers, P. 0.

Box 410, St. Joseph, Mich. 49085. $1.50.

3.4. Trapezoidal Flumes with Bottom Slope

The main advantage of flumes with trapezoidal section is that they have much larger

capacities than rectangular flumes of the same bottom width. One trapezoidal flume

the cutthroat type -- has already been alluded to in ref. 3.3.2.2. A trapezoidal flume

recommended by the U. S. Geological Survey incorporates a 5 percent bottom slope to create

supercritical flow, as shown in figure 3.3. Discharge curves are shown in figure 3.4,

reproduced from ref. 3.9.2. Data for 1-ft and 3-ft flumes only are available. No accu- racy statements are available.

3.5. Critical-Depth Flumes

3.5.1. Background

The trapezoidal critical-depth flume is shown in figure 3.5. In a sense it belongs in

the same category as the Palmer-Bowlus flume, since the flow can be predicted analytically

using critical-flow principles. In this case the long parallel throat permits the flow to

closely approximate parallel critical flow. Friction effects, i.e., head loss along the

flume and velocity distribution in the throat are accounted for in the theory (as closely

as possible) and flume ratings have been computed (3.5.2.1) for a selected group of flume

geometries covering a variety of channel conditions encountered in the field. Accuracy of + 2 percent is claimed for these solutions.

Rectangular critical flow flumes are described in ref. 3.5.2.2. Again these in principle belong with the Palmer-Bowlus flumes, but the inlet and outlet geometry is more detailed and discharge coefficients are more closely determined analytically.

3.5.2. General Information Sources

3.5.2.1. Replogle, J. A., "Critical-Depth Flumes for Determining Flow in Canals and

Natural Channels," Trans. Amer. Soc. Agric. Eng., 14, 3, 1971, pp. 428-433, 436.

Copy available from American Society of Agricultural Engineers, P. 0. Box 410,

St. Joseph, Mich. 49085. $1.50.

3.5.2.2. British Standards Institution, Standard No. 3680-4A, "Methods of Measurement of

Liquid Flow in Open Channels: Part 4A, Thin Plate Weirs and Venturi Flumes,"

1965. Order from American National Standards Institute, 1430 Broadway, New York,

N. Y. 10018. $9.50.

3.6. San Dimas Flume

3.6.1. Background

The San Dimas flume was developed specifically to pass large amounts of sediment and

debris. The original design is shown in figure 3.6 along with rating curves. Later modi

fications are covered in ref, 3.6.2.1.

3.6.2. General Information Sources

3.6.2.1. Bermel, K. J,, "Hydraulic Influence of Modifications to the San Dimas CriticalDepth Measuring Flume," Trans. Amer. Geophys. Union, 31, 5, Oct. 1950, 763-770.

Engineering Societies Library, 345 E. 47th St., New York, N. Y. 10017. $0.25

plus $3.00.

18
19
20
r

Flow

A - A B - B

i

A

_f

Figure 3.5. A trapezoidal critical depth flume.

5.0 4 0

3.0

•2.0

o

i-i j:u

:^08

lo.6

^ 04

w

tn

0)U 02

0.1

L=R + 2h

30'

"7

Stilling well

intoke: hole or slotU

NOTE: Solid curves ore defined by general equation:

Q - 6.35 w'°''H'^'"whece n -- 0.179 W°^^

Pressure heads in stilling well and depths

in flume are generally comparable

Ratings ore for free-fall conditions only.

. maximum flow

n = PLAN

010 020 040 060 10 20 40 60 100 200 300

Discharge, ft /s

Figure 3.6= Original San Dimas flume, from ref. 3.9.2.

21
This paper covers changes in ratings due to changes in floor slope, roughness, and errors due to partial blockage of the approach channel by debris.

3.7. H-Flumes

The H-flume was developed by the Soil Conservation Service, U. S. Department of Agriculture (3.9.3). Its principal advantage is simplicity of construction, as can be seen in

figure 3.7. Rating data are shown in table 3.3. No accuracy information is available.

3.8. Errors

For those flumes for which an estimate of the accuracy of the head discharge equations

or curves are given, this error can be combined with the head measurement error (estimated

by the user) to give a combined or system error. See section 2.4.8. for a discussion of

this type of estimate.

3.9. References

3.9.1. Walker, W. R. , Skogerboe, G. V., and Bennett, R. S., "Flow Measuring Flume for

Wastewater Treatment Plants," Jour. Water Poll. Control Fed., 45, 3, March 1973,

pp. 542-551.

3.9.2. Kilpatrick, F. A., "Use of Flumes in Measuring Discharge at Gaging Stations,"

Book 1, Chap. 16 of Surface Water Techniques , U. S. Geological Survey. Now under

revision. Original version out of print.

3.9.3. "Field Manual for Research in Agricultural Hydrology," Agriculture Handbook No. 224,

AgriCo Res. Serv. , Soil and Water Conserv. Res. Div. , reprinted 1968.

3.9.4. "Field Manual for Research in Agricultural Hydrology," Agriculture Handbook No.

224, reprinted 1968, Soil and Water Conservation Research Division, Agricultural

Research Service, U. S. Dept. of Agriculture.

Table 3.3

Discharge (cfs) for Selected H-Flumes

from Reference 3.9.3

Flume Type and Size, D

Head

ft

Type HS Type H Type HS

0.4 0.6 0.8 1.0 0.5 0.75 1.0 1,5 2 0 2.5 3,0 4.5 4.0

0.05 0.0010 0.0014 0.0017 0.0021 0.002 0.003 0.004 0.006 0.007 0.009 0.010 0.015 0.03

0.10 0.004 0.005 0.006 0.007 0.010 0.013 0.015 0,020 0.025 0.030 0,035 0,050 0.09

0,20 0.018 0.021 0.024 0.027 0.04 0.05 0.06 0.07 0,08 0.10 0.11 0,16 0.28

0.30 0.044 0.049 0.054 0.060 0.11 0.12 0.13 0.16 0.18 0.21 0.23 0,31 0.56

0.40 0.085 0.092 0.10 0.11 0.20 0.22 0.24 0.28 0.32 0,36 0.40 0,52 0.94

0.50 0.15 0.16 0.18 0.35 0.37 0.40 0.45 0.51 0.56 0.62 0.78 1.42

0.60 0.23 0.24 0.26 0.57 0.60 0.67 0.74 0.82 0.89 1.11 2.01

0.80 0.47 0.50 1,16 1.27 1.38 1,49 1.60 1.94 3.53

1.00 0.82 1.96 2,09 2,25 2,41 2.57 3,04 5.56

1.20 3.20 3.38 3.59 3.80 4.42 8.06

1.40 4.60 4.82 5.06 5,33 6.11 11.2

1.60 6.58 6.84 7.16 8.12 14.9

1.80 8.67 8.98 9.33 10.50 19.2

2.00 11.1 11.5 11.9 13.2 24.3

2.50 19.4 19,9 26.6 39.9

3.00 31.0 32.7 60.3

3.50 46.8 85.9

4.00 63.9 117

4.50 84.5

22
cV£

c ' O lA o o O 1 X £ o ' V ' a , ... - a SI

O - CO Kl r- c^J ?

'~

O CO 1 00

lO a>

o odd23
4. THIN PLATE WEIRS

4.1. Background

The weir shapes in most common use are rectangular, 90-degree V-notch, and trapezoidal.

These are shown in figure 4.1.

4.1.1. Rectangular Weirs

The rectangular weir crest can be in the form of a notch (figure 4.1a), i.e., a "contracted" weir, or it can span the entire channel width (figure 4.1b) in which case it is

called a "suppressed" weir. For the weir to operate as a "standard" contracted weir, the

side contractions should be at least twice the head and not less than 1 foot, and the crest

height should be at least twice the head and not less than 1 foot. Heads less than 0.2 ft

should not be used.

Francis equations . The Francis formulas below are frequently used for rectangular

weir discharge.

Suppressed weir: Q = 3.33H''''^L [4.1a]

Fully contracted weir: Q = 3.33H^*^(L - 0.2H) [4.1b]

where Q is flowrate (cubic feet per second), H is the height of water above the crest elevation at the measuring station (ft) and L is the weir crest length (ft). In both equations the velocity of approach can be included by replacing H^-*^ with

(H + h)^*^ - h^'^

where h is the approach velocity head V /2g. This correction usually is made by trial.

Solutions to eqs. 4.1 in tabular form can be found in refs. 4.3.1 and 4.3.5, and in other

sources. The Francis equations have the advantage of convenience even where tables are not

available, because of the constant coefficient. They should not be used for H > L/3, nor should eq. 4.1b be used for contractions which are less than standard (figure 4.1).

Kindsvater-Carter equation . This equation is coming into more frequent use and is

considered by some to be more accurate than the Francis formula.

Q = C L H [4.2]

e e e

where H = H + 0.003.

e

Lg = L + k|^5 with as given in figure 4.2a.

Cg = a coefficient as given in figure 4.2b.

An advantage of eq. 4.2 is that the velocity of approach effect is incorporated in the curves and need not be included by trial. Also, contractions less than standard can be

accounted for.

Eqs. 4.1 and 4.2 are compared in section 4.4.2.1.

4.1.2. V-Notch Weirs

Triangular or V-notch weirs (figure 4.1c) are particularly useful for low flows.

Standard contraction requirements are the same as for rectangular weirs.

Cone formula . This formula is for 90-degree fully contracted V-notches only.

Results are given in tables in ref. 4.3.1.

Q = 2.49h2-^® [4.3]

24
Note: Contractions > 2H; P> 2H, for

full contraction

Figure 4.1a. Fully contracted rectangular weir.

Channel walls

Figure 4.1b. Suppressed rectangular weir.

« B * \ / 90°--\/

AH

P

Figure 4.1c. V-notch 90 degree weir.

25
Sharp corner

0.03 in. to 0.08 in. (max.)

45° chamfer if plate

exceeds o.o8 in. thickness

Figure 4.1e. Weir edge detail.

26
0.020

0.010

0

0.010

-0.003

0 0<,20 0.40 Oo60 0.80 loOO

L/B

Figure 4.2a. Values of for eq. 4.2, from ref. 4.3.1.

4.2

4o0

3.8

3.6

3.4

3.2

3.0

L/B =

1 l.Ov^

3.22 + 0.40H[/P .

0c4/

0,2^

0 0.4 0.8 1.2 1.6 2.0 2.8

H/P

Figure 4.2b. Values of for eq. 4.2, from ref. 4.3.1.

27
Kindsvater-Shen . The basic equation, which is valid for' any notch angle is

Q = (8/15) (2g)l/2c tan (9/2) H

3/2 [4,4] e e where: G is the notch angle.

is measured head H plus K^, a factor given in figure 4.3.

Cg is a coefficient given in figure 4.4. Values of for incomplete contractions are given in figure 4.5 for 90-degree notches only . Equations 4.3 and 4.4 are compared in section 4.4.2.2.

4.1.3. Cipolletti (Trapezoidal) Weirs

The Cipolletti weir (figure 4. Id) is frequently found in field practice and has the same contraction requirements as rectangular weirs. Its equation is, without the velocityof -approach factor,

Q = 3.367 L H^-^ [4.5]

Tabular solutions to eq. 4.5 are given in ref. 4.3.1. Use of the Cipolletti weir with

eq. 4o5 does not give results as accurate as do the rectangular and triangular weirs

(4.3.1). Information is not available with which to estimate accuracy limits.

4.2. Uses

Weirs have the advantage of being relatively simple to construct and install, although

it should be emphasized that this simplicity does not imply that lack of care and precision is tolerable. Another advantage is that a considerable data base exists, although not

all results are in agreement. Their main disadvantage is the collection of solids behind

the weir plate, which if allowed to continue, ultimately will affect the head-to-crest

height ratio, H/P, and thus the discharge. They are nevertheless frequently used as temporary gaging stations in sewers, with apparent success if the installations are carefully

monitored for crest condition and upstream deposits.

Thin plate weirs also impose an appreciable head loss, which is undesirable or intolerable in some applications.

4.3. General Information Sources

4.3.1. "Water Measurement Manual," Bureau of Reclamation, U. S. Dept. of the Interior,

Second Ed., Revised reprint, 1974, Ch. 2, pp. 7-42. Order from U. S. Govt.

Printing Office, Washington, D. C. 20402. $5.80. Stock No. SN2403-0027, Cat.

No. I 27.19/2:W 29/2.

This reference contains considerable general background information on weirs,

a limited amount of information on construction and maintenance, head-discharge relations in tabular form for eqs. 4.1a, 4.3 and 4.5, curves for eq.

4.2, recommended weir box sizes and other useful information.

4.3.2. "Fluid Meters -- Their Theory and Application," H. S. Bean, ed., ASME Research

Committee on Fluid Meters, Sixth Edition 1971. Obtain from Amer. Soc. Mech.

Engrs., 345 E. 47th St., New York, N. Y. 10017. $20.00.

This source gives curves for application of eqs. 4.2 and 4.4. Principles of

weir flow are discussed, but there are no details on construction, head mea- surement, etc.

4.3.3. British Standards Institution, Standard No. 2680-4A, "Methods of Measurement of

Liquid Flow in Open Channels: Part 4A, Thin Plate Weirs and Venturi Flumes," 1965.

Order from American National Standards Institute, 1430 Broadway, New York, N. Y.

10018. $9.50.

28
0.60

0.58

0.56 -

0 20 40 60 80

Notch angle, degrees

100 120

Figure 4.4. Values of for eq. 4.4, from ref. 4.3.3.

29
Figure 4.5. Values of C for eq. 4.4, incomplete contract

tions, from ref. 4.3.3.

0 1 2 3 4 5

V, ft per sec

Figure 4.6. Upstream velocity distributions ( see 4.4.6 ).

30
This standard gives curves for application of eqs. 4.2 and 4.4. Many details

are given on requirements for accurate measurements, and on estimation of

measurement errors.

4.3.4. ASTM Standard D2034-68, "Open Channel Flow Measurement of Industrial Water and

Industrial Waste Water by Weirs." Order from American Society for Testing and

Materials, 1916 Race St., Phila., Pa. 19103. $1.50.

This standard provides a concise treatment of weirs, but some of the recom- mended discharge formulas are more complex than those heretofore cited in this

chapter. A convenient table is presented giving recommended weir and weir box

geometries for specific ranges of discharge. Details on float well construction and on depth sensing and recording instruments are given.

4.3.5. "Planning and Making Industrial Waste Surveys," Ohio River Valley Water Sanitation Commission, Cincinnati, Ohio, 1952. $2.00.

This report gives a very basic and well-illustrated introduction to weir

measurements. Flowrates are given in terms of gallons per minute in tables

for rectangular and 90-degree notch weirs.

4.3.6. Thomas, C. W. , "Errors in Measurement of Irrigation Water," Proc. ASCE, 83, IR3,

Proc. Paper 1362, Sept. 1957, 14 pp. Obtain from Engineering Societies Library

345 E. 47th St., New York, N. Y. 10017. $0.25 per page plus $3.00.

Errors due to incorrect geometries and head measurement are given in curves

for Parshall flumes and weirs.

4.4. Error Sources in Weir Use

4.4.1. General

As is true for all flow measuring devices, the accuracy of the result depends upon the

performance of the instrument treated as a system -- in this case (a) the primary element

(weir), (b) the secondary element (depth sensor and recorder), and finally (c) the manner

in which these elements are installed and maintained. The following sections deal with

these three aspects.

4.4.2. The Head-Discharge Relations

4.4.2.1. Rectangular Weirs

Of the many published rectangular weir formulas, only eqs. 4.1 and 4.2 are included

in this chapter, the first because it is so popular currently, and the second because it

appears to be acquiring more acceptance and is generally considered to be very accurate.

The two equations can best be compared by using numerical examples.

If there should be significant differences between the results of the two equations,

one can consider the range of the experiments from which the equations were derived.

Francis' experiments were on long crests, mainly 10 ft, with heads not exceeding 2 ft.

Kindsvater and Carter, on the other hand, used crest lengths of 0.1 to 2.7 ft and heads

from 0.1 to 0.75 ft.

Example 1 . Fully contracted weir; head, 0.50 ft; length 2.00 ft; channel width,

5.00 ft; crest height, 2.00 ft.

From eq. 4.1b: Q = 2.24 cfs

From eq. 4.2: Q = 2.26 cfs

Example 2 . Suppressed weir; head, 0.50 ft; length, 2.00 ft; crest height,

2.00 ft.

31
From eq. 4.1a: Q = 2.35 cfs

From eq. 4.2: Q = 2.36 cfs

Example 3 . Suppressed weir; head, 1.00 ft; length 10.00 ft; crest height = 2.00 ft.

From eq. 4.1a: Q = 34.2 cfs (including velocity-head correction).

From eq. 4.2: Q = 34.4 cfs

These results for weirs of reasonable dimensions agree within 1 percent. To illustrate the error that can be involved in using the Francis contracted weir formula (eq,

4.1b) on a weir which is not fully contracted, consider the following example.

Example 4 . Partially contracted weir; head, 0.50 ft; length, 2.00 ft; channel

width, 3.00 ft; crest height, 0.50 ft.

From eq. 4.1b: Q = 2.30 cfs (including velocity-head correction)

From eq. 4.2: Q = 2.39 cfs

The difference here is approximately 4 percent.

Note . Do not upe eqs. 4.1 for heads larger than one-third the crest length, even if such

results are included in published tables. Data reported in ref. 4.3.1 show that, at least

for short weirs, significant errors can result. For example, a fully contracted weir 2 ft

long with a 1 ft head had a measured discharge of 6.31 cfs. Equation 4.1 gives 6.00 cfs

(an error of -5 percent), while eq. 4.2 results in about 6.35 cfs (an error of less than

1 percent).

Errors due to failure to correct eqs. 4.1 for the velocity of approach at the head

measurement section can be computed by trial. They are tabulated in ref. 4.3.6 and are abstracted in table 4.1 below for purposes of illustration. Reference 4.3.1 contains

tables of three-halves powers of numbers to facilitate making this correction.

Table 4.1

Percentage Error in Q When

Francis Equations are Uncorrected

for Velocity of Approach

Measured Head, H, ft

0.2 0^_6 1.0

V, ft/sec Error in Q, %

0,5 2.7 0.9 0.6

1.0 9.8 3.4 2.2

1.5 20.8 7.5 4.7

It is seen that approach velocities have to be well below 0.5 ft per second before

the error becomes negligible at low heads. The use of eq. 4.2 obviates the need for the

velocity-of-approach correction.

4.4.2.2. Triangular Weirs

Contraction errors . Equations 4.3 and 4.4 give results within about 0.5 percent of

each other for 90-degree fully contracted weirs. However, if contractions are incomplete,

errors can result from use of eq. 4.3.

32
Example: 90 degree notch, H = 1.00 ft, P = 1.00 ft, B = 2.50 ft (see figure

4.1c). In this case the contractions are only 0.25 ft at the water surface.

From eq. 4.3: Q = 2.49 cfs

From eq. 4.4: Q = 2.57 cfs

The difference is more than 3 percent.

For angles other than 90 degrees, use eq. 4.4. Corrections for incomplete contractions

are available only for 90 degrees, however.

Angle measurement errors . A change of only 1 degree for a nominal 90 degree notch

would introduce an error of almost 2 percent in flowrate, through its effect on the tan

9/2 term in eq. 4.4, even the effect on Cg from figure 4.4 would be negligible. Therefore

the notch angle must be accurately determined.

4.4.3. Errors Due to Weir Plate Imperfections

Edge Sharpness . Rounding the upstream edge of the weir increases the flowrate.

Small amounts of rounding can occur in an initially "sharp" edge as a result of erosion

and wear. Schoder and Turner (4.8.2) presented data on roundness effects. An example is

given in Table 4.2 below.

Table 4.2

Approximate Percentage Change in Q Due to Edge Rounding

Radius of Round Head Discharge Change

in. ft %

0.016 0o2 0.8

0.016 0.6 0.6

0.016 1.0 0.3

0.042 0.2 2.2

0.042 0.6 1.2

0.042 1.0 0.5

0.125 0.2 6.0

Roughness . According to experiments cited in ref. 4.8.2, roughening the upstream

face of a rectangular weir to the texture of a rough file can increase flowrate by about

1.5 percent at 0.5 ft head and about 1 percent at a 1.25 ft head. Another set of experiments cited in the same reference indicated that a V-notch weir (angle not stated) with

a 3-inch head would have the flowrate increased by 1.8 percent if the initially smooth

brass weir plate were coated vn.th a medium emery, and by 2.4 percent if coated with coarse

emery.

The effects of edge rounding and plate roughening are in the same direction, increasing the flow for the same head. Therefore possible effects of aging and wear on weir

plates must be closely monitored.

4.4.4. Aeration of Suppressed Rectangular Weirs

Failure to provide sufficiently large air vents beneath the nappe of a suppressed

rectangular weir causes an increase in discharge. As an indication of the magnitude of

the potential error, a pressure of 1.2 in. of water (below atmosphere) beneath the nappe

caused a 5 percent discharge increase at 0.5 ft head (4.3.6). A method of computing the

air requirement can be found in ref. 4.8.1.

33
4.4.5 Errors Due to Weir Slope

If there is transverse slope to a rectangular weir, a systematic error in head can be

introduced, depending upon what part of the crest the head gage has been referenced to. Apparently weirs are not very sensitive to small upstream or downstream slopes of the

plate (4.3.6).

4.4.6 Upstream Velocity Distribution Effect

Examples of acceptable upstream velocity distributions are given in ref. 4.3.3. In

figure 4.6 are shown two velocity distributions which cause a discharge difference of about

3.5 percent for the same head on a suppressed weir as presented by Schoder and Turner

(4.8.2). Distribution B was deliberately created with artificial barriers. The a factors

are about 1.2 and 2.1 for A and B, respectively. However, the velocity distribution error cannot be generalized, except to say that it can be minimal if the velocity distributions

are in the range found in approach channels which are reasonably smooth, long and regular.

Additional examples of velocity distribution effect can be found in ref. 4.8.2. In general

the weir performance becomes more sensitive to velocity distribution as the head-weir

height ratio increases.

4.4.7. Supercritical Flow Channels

If the channel flow is supercritical, the weir has to be high enough to cause a hydraulic jump upstream. Reference 4.3.3 recommends that the jump be upstream a distance

of at least 30 times the maximum head.

4.4.8, Errors in Head Measurement

The comments in section 2.4.3 on head measurements for Parshall flumes are also valid

for weirs. An additional factor here is that for triangular weirs, in which discharge

varies with head to the five-halves power, errors in head measurement are correspondingly

more important in determining the total system error.

4.4.9. Combined (System) Error

The foregoing sections have called attention to a number of possible error sources

as an aid to the user in identifying some of the error components which contribute to the

total error of the measurement. However, as discussed in the Introduction and in section

2.4.8, the estimates given usually will not account for all the factors which enter into

field performance, particularly those associated with maintenance, aging and wear. Readers are referred to section 2.4.8 for discussion and an illustrative example (for

Parshall flumes) which can be adapted to thin plate weirs.

4.5. Weirs in Circular Channels

V-notch and contracted rectangular weirs as described in section 4.1 are frequently

installed in sewers or other circular conduits. For the sake of additional information,

work by Diskin (4.8.3) is cited here, in which several types of thin plate weirs were installed at the end of a circular pipe. These weirs included a "suppressed" (horizontal

crest) weir across the conduit, vertical slots, V-notches with apex at the pipe invert^ and

trapezoids starting at the pipe bottom. Diskin' s experiments included only one pipe diameter, 10 inches.

In connection with weirs for sewer gaging, Mort (4.8.4) describes a few practical

items, such as a method for shaping bulkheads to fit a sewer and a device to help set the

head zero.

4.6. Maintenance

Frequent cleanout of debris collected behind a weir and on the crest edge is imperative. Solids accumulated behind the weir in effect raise the bottom and introduce errors associated with increased values of H/P.

34
-^e 1

Measure head 2 to 3 H. from weir face max

Recommended limits on geometry (ref. 5.3.2.)

H > 0.2 ft

b > 1 ft

P > 0.5 ft

0.08< H/L< 0.85

0.18< H/(H + P) < 0.6

Tailwater energy level above crest should not

exceed 2H-/3 for free flow.

Figure 5.1a. The square-edge broad-crested weir.

35
*Head measured 2 to 3 H

1 from weir face

Recommended limits on geometry (ref. 5.3.2. )

H> 0.2 ft (or 0.03L, whichever larger)

Hj^/P < 1.5

H^^/L < 0.57

P > 0.5 ft

B •„ is largest of Hi , L/5 or 1 ft min ° J-max'

Maximum submergences, h/H-|^ , for free flow

Vertical. downstream face:

Hi/P'< 0.5, h/Hi 0.66

Hi/P'a? 0.5, h/Hi ^0.75

Hi/P'> 1.0, h/Hi 5= 0.80

Sloping downstream face:

Add 0.05 to above values of h/H

Figure 5.1b. The rounded-edge broad-crested weir

36
ISwM>OH

CM I CO

13 • nj lo oU •

(U

o

u

u

C

rH -H

0)

(3 -a R (U

n) t3

XI

C

•H0 to O cfl

13 -H o <u

•d ^ o Id

0) (U M 4-1 4J CO e (u O h o u 3

60

•H

Fi4

37

4.7, Field Calibration

1. By current meter (see Chapter 8). Often the velocities in the weir box immediately

upstream of the weir will be too low for accurate calibration by velocity traverse. In

example 1 of section 4.4.2.1, the approach velocity is 0,18 ft per second. Therefore any

velocity traverse would have to be made in a higher velocity section of the main channel

upstream or downstream.

2. By dilution methods (see Chapter 9).

4.8. References

4.8.1. Johnson, J, W, , "The Aeration of Sharp Crested Weirs," Civil Engineering, 5, 3,

1935, pp. 177-178.

4.8.2. Schoder, E. W. and Turner, K. B., "Precise Weir Measurements," Trans. Amer. Soc.

Civ. Eng., 93, paper 1711, 1929, pp. 999-1190.

4.8.3. Diskin, M. H. , "Sharp Crested Weirs for Circular Channels," Water and Water Eng.,

75, Aug. 1971, pp. 309-313.

4.8.4. Mort, S. F. , "The Practical Gaging of Dirty Water and Its Application to Sewer

Design," Proc. Inst. Civ. Eng., 1955, Part 3, No, 1, pp. 81-113.

5. BROAD-CRESTED WEIRS

5.1. Background

Broad-crested weirs have not been used for flow measurement in this country as extensively as thin plate weirs and Parshall flumes. Nevertheless they have certain advantages

and applications (see section 5.2) which warrant discussion.

The broad-crested weir can be rectangular, triangular or trapezoidal in lateral

section. Only the rectangular sections will be considered here. A cross-section in the

flow direction can be either a rectangle, i.e., a square-edge weir, or a rectangle with

rounded upstream corner. See figure 5.1.

5.1.1. Square-Edge Broad-Crested Weirs

The flow over square-edge broad-crested weirs can occur in different regimes (5.1),

depending upon the weir head-to- length ratio, H/L. See figure 5.2.

The usual "broad-crested" weir range for square edges is shown in figure 5.2c and

prevails for H/L between about 0.1 and 0.4. In this range there exists essentially parallel flow over most of the crest. However, the upstream sharp edge is the control point.

The flow passes through a critical condition in that region and remains supercritical

everywhere downstream. If H/L becomes smaller than about 0.1, the flow has the length

needed to change back to subcritical, and the control shifts to the downstream overfall.

This range is sometimes called the "long-crested weir." If H/L is larger than 0.4, the

flow becomes curvilinear throughout. The limiting H/L values given in figure 5.2 are approximate and will vary somewhat with flow and weir conditions.

The basic broad-crested weir equation is

Q = (2/3) (2g/3)^^^Cj^bH^^^^ = C^bH^^^^ [5.1a]

or Q = (2/3) (2g/3)^^^CpC^bH^^^ = CbH^^^ [5.1b]

2 3/2

C = (1 + aV /2gh) '

39
where b is the weir width (transverse to the flow direction), H^is the total head (measured head H plus the effective approach velocity head). The coefficient is empirical

in the case of the square edge weir and is often combined into the overall coefficients C

and C^; however, in rounded edge weirs, C accounts for frictional effects and can be

estimated analytically (see section 5.1.2).

The user is cautioned, when using published coefficients, to note whether they are actually C or C^^. In this section all values are based on total head. A successive approximation procedure is required to convert from measured head, H, when approach velocity is

appreciable, but use of is somewhat more frequent in publications.

In the broad-crest range (0.1 < H/L < 0.4, approximately) C is a constant at 2.62 +

0.08, provided H/P is between 0.22 and 0.56 (5.3.2). P is the crest height above the channel floor. Some supporting data are shown in figure 5.3. This Ci is for ft-sec units only.

In the range H/L > 0.4, recommended coefficients are given in figure 5.4 (5.3.2), For

the most part, available data represent tests for H/P less than about 1.0, and application

should be restricted accordingly.

In the long-crest range (H/L < 0.1) published results differ, and the square-edge weir

is in reality not well-suited for this range. Readers can find results in refs. 5.9.1 and

5.9.3.

The fact that there is considerable scatter and discrepancy in published results for

the square-edge weir is not surprising. For H/L > 0.1 the upstream corner is the control.

Therefore the results will be subject to effects due to lack of sharpness, roughness, etc.,

just as for thin plate weirs. At H/L < 0.1 the sharpness of the edge comes into play as an energy loss mechanism, as does the roughness of the weir surface. The user should consider

these factors when applying published results.

5.1.2. Rounded-Edge Broad-Crested Weirs

In the rounded-edge broad-crested weir (figure 5. lb) the nose radius should be at

least 0.2H (5.3.2) in order to prevent separation. Then the control point is at the

overfall ani^ydrostatic critical flow exists near the overfall in the nearly parallel

part of the flow, and it can be shown theoretically that

= (2/3)^^^g^^^(l - 26^/b) (1 - 6^/H)^^^ [5.2]

Here 5^ is the boundary layer displacement thickness, which is described in all fluids

textbooks and which is also discussed in ref. 5.3.1. A good analytical determination of C^^ therefore requires an estimate of the weir roughness and of the location of transition

between laminar and turbulent flow in the boundary layer (5.3.1). Reference 5.3.2 suggests a method for estimating S ^ in terms of crest length so that the user does not have

to resort to the boundary layer equations.

5.2. Uses

The square-edge broad-crested weir is simple in configuration and easy to build. It

has a certain structural stability which thin plate weirs lack and permits a higher downstream water level without submergence effects than does the thin plate weir. On the other

hand, it also possesses the main disadvantages of the thin plate weirs -- trapping of

debris, sensitivity of discharge to edge and crest condition, and susceptibility to leadingedge damage.

Therefore, although much of the past research was concerned with the square-edge weir,

there appears little reason to favor it over the rounded-edge broad-crested weir, particularly when one adds the consideration that the latter is amenable to analytical treatment

over a considerable flow range (H/L < 0,4). See ref, 5.3.1. A rounded-edge broad-crested

weir is similar to a rectangular flume with raised floor.

40
0

0

0

0

o O

0 0 0

0^

P 00/ 0

^ 0

o

9,0

° 0

0 /

0 /

0

0

0° ^

-o-J

— 0

(5) CP

0

0 0

Data of Bazin, Rafter, Woodburn , Doerinsf eld

Kikkawa and U.S.G.S.

See Ref. 5.9.2. H/(H + P) < 0.35

0 0.25 0.50 0.75 1.00

H/L

Figure 5.3. Discharge coefficient data for square-edge broadcrested weirs, ft-sec units.

Figure 5.4. Discharge coefficients for square-edge broadcrested weirs including head-to-weir height

ratio, from ref. 5.3.2.

41
5.3. General Information Sources

5.3.1. Harrison, A, J. M. , "The Streamlined Broad-Crested Weir," Proc. Inst. Civ. Engrs.,

38 , 1967, Paper No. 7028, pp. 657-678. Obtain from Engineering Societies Library,

345 E. 47th St., New York, N. Y. 10017. $0.25 per page plus $3.00.

This paper gives an analytical treatment and reviews available data for weirs

with rounded upstream corner.

5.3.2. British Standards Instituti on, Standard No. 3680-4B, "Methods of Measurement of

Liquid Flow in Open Channels, 4B: Long-Base Weirs," 1969. Order from American

National Standards Institute, 1430 Broadway, New York, N. Y. 10018. $7.00.

This standard gives many details on the installation, use and determination of

coefficients for broad-crested weirs. It also includes the triangular (Crump)

weir, which has not yet been widely used in the United States.

5.4. Error Sources

5.4.1, General

The accuracy of the final measurement depends upon the performance of the instrument

as a system -- (a) the primary element (weir), (b) the secondary elements (depth sensor

and recorder), and finally (c) the manner in which these elements are installed and maintained. This section and the following sections deal with these aspects.

5.4.2. Head-Discharge Relations

Square-edge weirs . Some of the available results for square-edge weirs are shown in

figure 5.3 and these data afford some idea of the expected precision. The British Standards Institution (5.3.2) suggests using the curves of figure 5.4 to extend the constant

coefficient C^^ = 2.62 to higher values of H/L. The error in head-discharge relation for

a carefully fabricated and installed square-edge weir can be estimated from

Error = + (lOF - 8) percent [5.3]

where F is as defined in figure 5.4.

Rounded-edge weirs . Some published results for the round-edge weir are shown in

figure 5.5. Reference 5.3.2 suggests an estimated error in the head-discharge relation of

a carefully fabricated round-edge weir of

Error = + 2(21 - ^OC^) percent [5.4]

where C^ = (1 - 26,/b)(l - 6,/H)^"^ [5.5]

D

The data of figure 5.5 substantiate that in regions of high C^^, i.e., H/L between about 0.2

and 0.5, the scatter is not large. It is emphasized that the error estimates of eqs. 5.3

and 5.4 should "he applied only to carefully fabricated weirs which are new. There is no way to assess the effects of aging and wear without direct field measurement.

5.4.3. Departures from "Standard" Geometry

Dimensions should be adhered to within 1 part in 400 (5.3.2). Of course differences

in weir width b are accounted for directly in the discharge equation, provided the sidewalls remain parallel.

Level . Downward slopes are often caused by settlement due to downstream scour in

earth channels. Rounded-edge weirs with downward slope will have the control point (critical depth) shifted from the overfall to the upstream end of the weir at some value of this

slope. This value of weir slope depends upon geometry and roughness but it can be as small

as 0.002.

42
(.00

0.90

C,

0.80

0.70

0.2

L = 2.5 2

+1

Transition Reynolds no. for theory, 3 x 10

© Bazin series 116

C Bazin series 117

O Woodburn

•O- Smith, L = 1 ft

)( Smith, L = 0.5 ft

+ De Marchi

Theory

0.4 0,6 0.8

H,/L

Figure 5.5. Discharge coefficient data for rounded-edge broadcrested weirs.

/P from toe permissible base max truncations

Figure 5.6. The triangular weir.

43
As an illustration of the error so introduced, in ref. 5.9.3 rounded-edge weirs with

low values of H/L were tested level and at slopes of 0.004 and 0.026. Comparing results

for H/L = 0.10 shows that discharge coefficients are increased over the level condition by

about 1.5 percent and 5.5 percent for the 0.004 and 0.026 slopes, respectively. No information is available for higher values of H/L.

5.4.4. Velocity Distribution Upstream

The effect of the upstream velocity distribution can be estimated analytically only for

those weir flows in which the control point (critical depth) is at the downstream brink,

i.e., mainly rounded-edge weirs and, to some extent, "long-crested" square-edge weirs. If

the approach velocity head is very small relative to the measured head, modest changes^in

approach velocity distribution will not have a significant effect. For example, if aV /2g

(see section 2.4.5) is less than .02H, even a 25 percent change in approach a will cause only a 0.5 percent effect on the head. For large values of velocity head, a rational cor- rection procedure for increased a is as follows. Assume that for the same Q, the overfall

conditions and therefore the total head at the overfall remain the same. Therefore, the

upstream total head, H^, should remain the same, ignoring small differences in energy

losses. However, the measured head, H, will decrease by an amount aV /2g as Oi is increased .

5.4.5. Errors in Head Measurement

These errors are the same as those encountered in flumes and thin plate weirs. See

section 2.4.3. See also ref. 5.3.2 for general instructions on head-measurement installations .

5.4.6. Combined (System) Error

The foregoing sections have indicated some of the error sources which contribute to

the total error of measurement. Estimates of combined error may be meaningful in evaluating the performance of new weirs which have been fabricated and installed in accordance

with recommended practices. However, errors due to aging, wear or less-than-optimum field

and installation conditions can best be determined through an independent and more accu- rate measurement on site. Users are referred to the Introduction and to section 2.4.8 for

additional discussion and an illustrative example of combined errors in Parshall flumes

which can be adapted to broad-crested weirs.

5.5. Triangular Weirs

Triangular weirs (figure 5.6) warrant mention in this chapter even though they are not,

strictly speaking, weirs with finite crest width. This type of weir is able to pass some debris and still retain some of the advantages of a sharp edge. Information on this weir

is available in ref. 5.3.2. The weir coefficient is

H< 0.5 ft: 1.150 (1 - O.OOl/H)'^''^ [5.6]

H > 0.5 ft: = 1.150 [5.7]

5.6. Installation

Broad-crested weirs should be installed so that they never become submerged, i.e., so that they operate independently of tailwater elevation change. Reference 5.3.2 gives details on the limiting downstream heads for achieving this condition.

Upstream of the weir, the channel should be straight and reasonably uniform for a distance of at least 10 b. If straightening vanes can be used, they should not come closer

than 10 H to the measuring station (5.3.2). If the channel is steep and flow is supercritical, the weir should be designed so that the hydraulic jump occurs at least 30 H

upstream (5.3.2).

A recommended convergence for installing weirs in wider channels is shown in figure

5.1c.

44
5.7. Maintenance of Weir Structure

The channel section upstream of the weir should be cleaned periodically of silt and

debris, and the weir itself must be checked for comer and surface damage. See 3.4.2.

5.8. Field Calibration

By current meter traverse (see Chapter 8).

By dilution methods (see Chapter 9).

5.9, References

Govinda Rao, N. S. and Muralidhar, D., "Discharge Characteristics of Weirs of

Finite Crest Width," La Houille Blanche, Aug. - Sept. 1963, pp. 537-545.

Harrison, A. J, M. , "Some Comments on the Square-Edged Broad-Crested Weir," Water

and Water Engineering, London, Nov. 1964,

Woodburn, J. G., "Tests of Broad-Crested Weirs," Trans. Amer. Soc. Civ, Eng., 96 , 1932, pp. 387-453.

6. PRICE AND PYGMY CURRENT METERS

6.1. Background

Vertical axis meters with rotating bucket wheels are popular for field use in this

country, so a separate chapter is being devoted to them. The principal instrument in this

group is the Price meter (figure 6.1). The Pygmy meter (figure 6,2) is, roughly speaking,

a two-fifth scale replica of the Price meter and was developed later for use in small channels. Many of the investigations of these meters have been performed by personnel of the

U„ S. Geological Survey and are thoroughly described in the publications of that agency,

some of which are referred to here.

Price meters can be rod mounted and used by a wader (or in the case of very small

channels, by an operator on a bank or bridging plank) or they can be suspended by a cable

and weight (see figure 6.3). The Pygmy meter is used only with rod mounting.

6.2. Uses

The most frequent application of this class of current meter is in the determination

of volumetric flowrate through a section by velocity-area integration. This procedure is

covered in Chapter 8; in this chapter only the performance characteristics of the current

meter itself are considered.

In comparison with horizontal-axis (propeller) meters the Price and Pygmy meters have

the following advantages:

1. Their threshold velocities are usually lower;

2o The lower pivot bearing operates in an air pocket, so the likelihood of silt

intrusion is reduced;

3. The Price meter in particular has earned a reputation for sturdiness and reliability under field use.

The main disadvantage of the Price and Pygmy meters is that they are not sensitive to

the angle of approach of flow in the horizontal plane. As an extreme example, these

meters rotate in the same direction and at almost the same rate for a downstream velocity,

V, and for an upstream velocity, -V, of the same magnitude. Also, the meters respond to

vertical components of velocity with the same direction of rotation, so that vertically

oscillating platform motions appear in the record as an apparent positive velocity. See

section 6.5.4 and ref. 6,6.2.

45

1.

2.

5,9,1.

5,9,2,

5,9,3.
Wheel di am. = 5 in

1. Cop for contact chamber

2. Contact ctiamber

3. Insulating bushing for contact

binding post 4. Single -contact binding post 5 Penta— contact binding post

6. Penta gear

7. Set screw

8. Yoke

9. Hole for hanger screw

10. Tailpiece

1 1 . Bolonce weight

12. Shaft

13. Bucket-wheel hub

14. Bucket-wheel hub nut

15 Raising nut

16 Pivot bearing

17. Pivot

18. Pivot-adjusting nut

19. Keeper screw for pivot-adjusting nut 20 Bearing lug

21. Bucket wheel

Figure 6.1. Price current meter, from ref. 6.3.3.

1 . Cop for contact chomber

2. Binding-post beaded wire

3. Binding-post insulating bustling 4. Binding-post body

5. Binding-post nut

6. Yoke

7. Yoke set screw

8. Upper bearing

9. Stioft

10. Bucket-wheel hub

I I . Bucket-wheel hub nut

12. Bucket wheel

13. Pivot bearing

14. Pivot

15. Pivot set screw

16. Pivot-adjusting nut keeper screw

17. Pivot-odjusting nut

Wheel diom. = 2 in.

Figure b.Z. i'ygmy current meter, from ref. 6.3.3.

46
Insulated copper and

stainless -steel core--'

Insulated lead wireNOTE

Suspension distonces listed below ore measured from horizontal axis of the meter to the bottom of the weight

along £ of hanger to the nearest tenth of a foot.

Jse this honger hole for suspension of

fo.g' above a i5-lb. wt

; 0.9 30-lb.

"

Type AA meters 0.9 50-lb. " -]<

I 1.0' " " 75-,IOO-, or 150-lb. weight.

Use this hanger hole for suspension of:

-r . . . ro.5' above a i5-lb. wt *

Type AA meter-i ^ „

' \0.5 50-lb.

Use this hanger hole for suspension of Type AA meter- 0.5' above a 30-lb. wt.;!<

>p Preferred suspension

Columbus-or C-Type weight- hanger -

i5-lb. weight I9|" long

30-lb. weight 21-5" long--,

50-lb. weight 23" long —

^'""Continued at"x" —Ellsworth coble

"-Lace connector

SHOWING

LACING

"-"--"-Golumbus-or C-Type weights

Figure 6.3a. Price meter with Columbus weight, from ref.

6.3.2.

Figure 6.3b. Price meter with Elliptic weight.

47
The Price meter is well-suited for use in natural streams and in artificial open channels (even those containing some silt) provided the measuring station and methods are chosen to minimize the disadvantages cited in the previous paragraph. Price meters have even reportedly been used in domestic sewage for very brief periods of immersion, although they

are generally considered more susceptible than propeller meters to fouling by large debris.

Pygmy meters are advantageous in small and shallow channels.

6.3. General Information Sources

Buchanan, To J. and W. P. Somers, "Discharge Measurements at Gaging Stations,"

Book 3, Chap. A8 of Techniques of Water Resources Investigations of the U. S. Geological Survey , 1969. U. S. Govt. Printing Office, Wash., D. C. 20402,

$0.70. Cat. No. I.19.15/5:bk 3, Chap. AS, S/N 2401-0498.

This document gives a good general overview of current meters and auxiliary

flow measuring equipment, their proper use and their application to streamgaging.

"Water Measurement Manual," Bureau of Reclamation, U. S. Dept. Interior, Second

Ed., Revised Reprint, 1974, Chap. 5, U. S. Govt. Printing Office, Wash., D. C.

20402. $5.80. Cat. No. 127 . 19/2 : W29/2 , S/N 2403-0027.

This reference reviews current meter application to streamgaging, and for

this purpose it could be used as an alternate to ref. 6.3.1 above.

Smoot, G. F. and Novak, C. E., "Calibration and Maintenance of Vertical-Axis Type

Current Meters," Book 8, Chap. B2 of Techniques of Water Resources Investigations

of the U. S. Geological Survey , 1968. U. S. Govt. Printing Office, Wash., D. C. 20402. $0.40. Cat. No. 119. 15/5 :bk. 8, Chap. B2, S/N 2401-0504. Note: This

document is being reprinted. Check price before ordering.

This document gives the most detailed information available on the actual

handling of meters for maintenance purposes, e.g., assembly, lubrication, etc.

Smoot, G. F. and R. W. Carter, "Are Individual Current Meter Ratings Necessary?",

Proc. Amer. Soc. Civ. Eng., 94, HY2, Mar. 1968, 391-397. Obtain from Engineering Societies Library, 345 E. 47th Street, New York, N. Y. 10017. $0.25 per

page plus $3.00.

This paper gives useful information on the effect of bearing wear on Price

meter performance and on the variability of calibrations of meters from the same and from different manufacturers.

6.4. Calibration

6.4.1. Calibration Equations

Price meters . Price meters are usually calibrated over the range 0.25 to 8.0 ft.

per second. The calibration curve of velocity, V, versus revolutions per second, N, can

be closely approximated by two straight lines intersecting at N = 1. For example, typical

calibration equations might be:

N < 1, V = 2. 198N + 0.017

N > 1, V = 2. 182N + 0.033

These results are sometimes closely approximated by a tabular chart for convenience.

A calibration equation is supplied by the manufacturer at the time of purchase. This

could be either a group average calibration equation or an individual calibration. Individual calibration curves (not the separate calibration points) which are run repetitively are repeatable to well within 1 percent over practically the entire velocity range. In ref.

6.3.4 it is shown that a group or batch calibration equation can adequately represent the

6.3,2.

6.3,3.

48
performance of individual Price meters from the same manufacturer. However, using an average or "class" curve for instruments of three manufacturers resulted in differences as high as 2 percent even for velocities greater than 0.5 ft per second. If accuracy of better than about + 3 or 4 percent is desired at the low end of the calibration range (V near

.25 ft per second) individual calibrations are desirable. The need for individual calibrations is increased if data are to be taken at velocities less than 0.25 ft. per second,

in which case the calibration velocities should be extended to below 0.25 ft per second.

Note: The U. So Geological Survey does not recommend use of these meters below 0.2 ft per

second unless absolutely necessary. See also section 6.5.6.

Pygmy meters . Pygmy meters are generally rated over the range 0.25 to 3.0 ft per

second, and the calibration curve is closely approximated by a single straight line equation, e.g.,

V = 0.970N + 0.030

Pygmy meters are sometimes used with a class calibration of V = N, where V is velocity

in ft per second and N is rate of rotation in revolutions per second. Although it appears

(based on limited data) that this might be accurate within about 3 percent or so for velocities higher than 1 ft per second, the velocities so obtained at 0.25 ft per second are likely to be considerably more in error and individual calibrations are recommended if

greater accuracy is needed.

Although conflicting opinions are reported in the literature, it appears that these

meters (Price and Pygmy) are not subject to significant temperature effects.

6.4.2. Maintenance of Calibrations

No quantitative guidelines for frequency of recalibration of current meters have been

published. According to Smoot and Carter (6.3.4) Price meters are not particularly sensitive to bearing condition, particularly at velocities higher than 0.25 ft per second. See

also section 6.5.1. One can assume that, if the meter passes the 4-minute spin described

in references such as 6.3.1, at least the meter assembly, bearing and contact friction are within tolerable limits. Pivot pins can be readily replaced in the field when necessary to reduce bearing friction.

On the other hand. Price meters are sensitive to dented cups (6.3.4). See also sec- tion 6.5.1. A meter with dented cups should be returned to the shop for rotor replacement,

after which it is preferable that the meter be recalibrated.

Field spin test recommendations are also available for Pygmy meters (6.3.1).

6.4.3. Method of Support

According to refs. 6.3.1 and 6.3.3, the calibration equations are the same for the

Price meter rod-mounted or suspended properly with a Columbus weight (figure 6.3). This

conclusion is essentially supported by limited comparative tests made by NBS (unpublished)

in which the differences in rod and cable (15 and 30 lb Columbus weights) ratings were less

than 1 percent provided that the velocity was greater than 0.75 ft per second. A larger

difference was indicated at the lowest velocities, but it is not certain yet whether this was a valid hydrodjmamic effect or a spurious result of the calibration procedure.

When the Elliptic weight series are used (figure 6.3) one meter manufacturer recommends a 2 percent velocity increase over that indicated by rod ratings.

6.4.4. Calibration Method

Meters are usually calibrated by towing them through still water in a towing tank.

Generally, two passes along the tank (in opposite directions) are made to cancel the

effects of drift currents. The stilling time between runs needed to limit the effects of

residual inertial currents has not been quantified.

49
There has always been a question as to whether a rating done in a towing tank properly

reproduces conditions in turbulent flowing water. Very intense and large scale turbulence

was generated by Yarncll and Nagler (6.6.1) by placing obstructions and paddles in a channel.

The Price meter over-registered significantly under these conditions, as would be expected

from the properties described in section 6.2. However, any station selected for current

meter traversing should be free of this kind of "turbulence," if there is any choice. Be- cause of the shape of the cups, there is probably little effect of very small scale turbulence, although there is no experimental verification for this statement.

2 Reference 6.6.4 suggests an over-registration for cup-type meters of about 0.2 (u/V)

where u is the rms longitudinal turbulence and V is the time average velocity. This result

pertains to low frequency turbulence, between 0.08 and 0.8 Hz, and for u small compared to

V. Application of this guideline would result in a predicted over-registration of about

0.5 percent for a 15 percent turbulence level. Pending a systematic and thorough investigation of this problem by comparative calibrations in water tunnels and towing tanks, the

safest policy is to select measuring stations which, at the least, have no obvious severe eddying motions or other evidence of intense, large scale turbulence. See also section

7.5.4.

6.5. Error Sources

6.5.1. Meter Condition Effects

Meter condition was mentioned in section 6.4.2 and quantitative information on Price

meter condition effects is available in ref. 6.3.4. To illustrate the size of these effects, a worn pivot point can cause a Price meter rating change of 4 percent at 0.25 ft per

second. However, at velocities greater than 1 ft per second, the change is not more than a few tenths of a percent. On the other hand, even "slightly dented" cups can cause an error

of close to 1 percent at high velocities, increasing to more than 3 percent at 0.25 ft per

second (6.3.4). Corresponding data for Pygmy meters are not available to the writers.

6.5.2. Turbulence Effects

Intense, large-scale eddying motions in the measuring section must be avoided because

the bucket-type meters will over-register in such flows (6.6.1). See section 6.4.4 for

additional discussion.

6.5.3. Rod Not Vertical

Data in ref. 6.6.1 indicate that the Price meter will not show any effects of rod tilt

in the vertical plane for vertical angles up to 5 degrees, at least for velocities over 2 ft per second. For larger angles, the effect depends upon whether the effective vertical

component of current is upward or downward on the meter. Curves can be found in ref.

6.6.1.

6.5.4. Platform Motion Errors

Vertical motions . Because the bucket-type current meters will rotate slowly in re- sponse to vertical relative motions, it is especially important to avoid such motions. An

example is the rocking of the platform in waves when cable-suspension measurements have to

be made from a boat. Data on vertical relative motions for Price meters are given by

Kallio (6.6.2). Errors from this source become more important as the horizontal velocity

decreases and the vertical velocities increase. For example, if the horizontal velocity

(to be measured) is 0.6 ft per second, there is a negligible error for vertical velocities up to about 0.3 ft per second, but the error approaches + 30 percent if the vertical

motions increase to 0.6 ft per second.

Horizontal motions . If a flow has horizontal axial oscillations superposed on it, the

meter can properly integrate the result provided that the oscillation frequency is sufficiently low and provided also that the oscillation amplitude is small enough so that

negative resultant velocities are not created. Some indication of "sufficiently low" frequency is available from limited data in ref. 6.6.1. A Price meter oscillating with 2 ft

stroke in a 2 ft per second flow began to over-register measurably at frequencies higher

50
than about 0.2 Hz.

However, transverse oscillations in the horizontal plane will cause over-registration

even at very low frequency. For example, a Price meter immersed in a 2 ft per second flow

but sinusoidally oscillating laterally in a + 0.5 ft excursion with a 10-second period

would record an average velocity 2.4 percent too high.

These platform motions can be considered to approximate the effects of large scale,

low frequency turbulence.

6.5.5. Boundary Effects

Price and Pygmy meters should not be used within 0.5 ft and 0.3 ft, respectively, of

the bottom. If used closer than these distances from the water surface, they will underregister. Also, there are limited data to suggest that they should not be used closer than

0.5 ft to the sidewalls. In general, the data available to provide corrections, should

these proscriptions be violated, are too limited for reliable application.

6.5-6. Very Low Velocities

If a Price meter has to be used at velocities less than 0.25 ft per second (and such

use should be avoided where possible), the calibration data should cover that range and

the meter condition should be carefully and frequently monitored with spin tests thereafter.

A routine calibration (to 0.25 ft per second) should never be extrapolated to 0.1 ft per

second unless the meter has unequivocally passed a 4-minute spin test. For example, in

unpublished NBS tests one Price meter with a 3-minute spin rotated 25 percent more slowly

at 0.1 ft per second than the same meter with a spin test close to 5 minutes.

6.5.7. Oblique Currents

If for some reason the flow at a measuring station is oblique (in a horizontal plane)

to the Price or Pygmy meter orientation, and the velocity directly in line with the meter

is desired, the meter angle of approach 6, should be measured. For small 9, a correction

can be made by multiplying the registered velocity by cosine 6, For larger 9, where yoke

orientation would have an effect, see ref. 6.6.1.

6.5.8. Wading

Although procedures are recommended for minimizing body interference on wading measurements, e.g., refs. 6.3.1 and 6.3.2, there are limited data which suggest that velocities

registered by waders might be about 2.5 percent too low (6.6.3).

6.6. References

6.6.1. Yamell, D. L. and F. A. Nagler, "Effect of Turbulence on the Registration of

Current Meters," Trans. Amer. Soc. Civ. Eng., 95, 1931, 766-860.

6.6.2. Kallio, N. A., "Effect of Vertical Motion on Current Meters," U. S. Geol. Survey

Water Supply Paper 1869-B, 1966. Uo S. Govt. Printing Office, Wash., D. C. 20404,

$0.15.

6.6.3 Schoof, R. R. and F. R. Crow, Discussion of "Are Individual Current Meter Ratings

Necessary?", Proc. Amer. Soc. Civ. Eng., 94, HY6, Nov. 1968, 1596-1601.

6.6,4. "Fluid Meters -- Their Theory and Application," Amer. Soc. Mech. Eng., 6th ed.

,

1971.

7. PROPELLER CURRENT METERS

7.1. Background

The most frequently encountered horizontal-axis current meters are the Neyrpic and Ott

type meters, both of which employ helical-bladed propellers. See figures 7.1 and 7.2.

51
These meters are very widely used in Europe and most standardization efforts by international groups are devoted to these or similar meters. In the U. S, they are used to some extent for streamgaging but more frequently for determinations of volumetric flowrates

through turbines and pumps.

The Haskell meter and the Hoff meter are propeller types which are occasionally used

in this country, the latter frequently for measuring pipe flow. However, there is little

recent technical information on them available in the open literature. See figure 7.3.

They are discussed very briefly in ref. 7.6.1 and some information on their behavior in

turbulence is given in ref. 6.6.1.

Propeller meters of the type commonly used in oceanographic studies are not included

in this chapter.

7.2. Uses

The principal advantage of the propeller current meters (relative to Price and Pygmy

meters) is that, with properly selected rotor, they can be relatively insensitive to

obliqueness of the approaching current, i.e., for small angles of approach such a meter

responds only to the component of velocity in line with the meter axis. (See section

7.5.5 for typical limitations.) This is the feature that makes them more suitable for

velocity traverses at turbine intakes where oblique velocities are often encountered.

The main disadvantage of the Ott and Neyrpic meters is that, at least in the opinion

of some users (ref. 7.6.1), they are not as sturdy under harsh field conditions as the

Price meter.

7.3. General Information Sources

7.3.1. I. S. 0. Standard No. 748, "Liquid Flow Measurement in Open Channels -- VelocityArea Methods," 1973. Order from American National Standards Institute, 1430

Broadway, New York, N. Y. 10018. $12.95.

This standard is concerned with the total problem of flowrate determination,

and it therefore has some sections on current meter use and the associated

probable errors.

7.3.2. British Standards Institution, Standard No. 3680-3, "Methods of Measurement of

Liquid Flow in Open Channels, Part 3: Velocity Area Methods," 1964. Order from

American National Standards Institute, 1430 Broadway, New York, N. Y. 10018.

$7.00.

This standard contains information similar to that of I. S. 0. Standard No.

748, ref. 7.3.1.

7.3.3. Jepson, P., "Currentmeter Errors Under Pulsating Flow Conditions," J. Mech. Eng.

Sci,, 9, 1, 1967, pp. 45-54. Obtain from Engineering Societies Library, 345 E. 47th St., New York, N. Y. 10017. $0.25 per page plus $3.00.

7.3.4. Johnson, R. L. , "Laboratory Determination of Current Meter Performance," Tech.

Rep. 843-1, Division Hydraulic Lab., U. S. Army Eng. Div. , North Pacific, 1966.

Available at no charge (while supply lasts) from Division Hydraulic Laboratory,

U. S. Army Engineer Division, North Pacific, Corps of Engineers, Bonneville, Ore

97008.

This report is a thorough documentation of one agency's experience in

determining propeller meter performance. Many factors affecting the calibration equations are discussed in detail.

7.4. Calibration

7.4.1. Calibration Equations

52
53
The calibration curves for Neyrpic and Ott meters are usually approximated by two

(and sometimes three) straight-line segments. For example, an Ott rating equation will

have the form

V = 0.4211N + 0.130, 1.00 < N < 12.08

V = 0.4264N + 0.066, 12.08 < N < 16.00

where V is velocity in ft per second, and N is rotation speed in revolutions per second.

The above is only illustrative; propeller current meters frequently are supplied with two

or more propellers of different pitch for use on the same bearings, and of course the nu- merical constants in the rating equations will change drastically with geometry.

Use of an average or group calibration is probably accurate within about 2 percent,

at least for velocities greater than 1 ft per second. However, analysis of data presented

by Johnson (7.3.4) for a group of Neyrpic meters suggests that the accuracy is less at 0.5

ft per second. Therefore, individual calibrations are recommended for low velocities. The

manufacturer claims 1 percent accuracy if meters are calibrated individually.

7.4.2. Maintenance of Calibrations

There is little in the literature concerning recommended frequency of recalibration

.

Reference 7.3.2 recommends that individually rated meters be re-rated after 100 hours of use. If they are not re-rated then, the group calibration should be used thereafter.

Manufacturers' maintenance instructions should be followed.

7.4.3. Method of Support

Although propeller meters can be used with both rod and cable suspension, there is no information in the literature about cable-suspended calibrations. Manufacturers' instructions on cable/weight as well as rod configurations should be followed closely. For ex- ample, for the particular vertical strut used in ref. 7.3.4 the Neyrpic meter rotated about

1 percent slower when the length of the horizontal sting was reduced from 34 inches to 13

inches

.

7.4.4. Calibration Method

Propeller current meters are usually calibrated in relatively still water in a towing

tank, but they are used in flowing water containing turbulent fluctuations of various

scales and intensities. The turbulence effect on propeller meters is the subject of con- tinuing research, and some indication of the upper limit of this effect is given in sec- tion 7.5.4.

7.5. Error Sources

7.5.1. Temperature

Many propeller meters have bearings which are immersed in oil. Temperature can affect meter performance by changing the viscosity of this lubricating oil. Therefore, it is

important that the temperature of meter calibration be known and taken into account. Similarly, manufacturers' recommended lubricating oils should be used. If this is not possible, the substitute oil should have a viscosity close to that of the recommended oil

(7.3.4).

For example, one particular meter in ref. 7.3.4 slowed about 1 percent at high

velocities when the temperature was reduced from 70°F to 40°F." At the lowest

velocity, however, the corresponding change was almost 4 percent.

Additional data on temperature effect are available in refs. 7.3.4 and 7.6.3.

54
7.5.2. Calibration Error

Calibrations made in different towing tanks, i.e., in different calibration laboratories, can yield different results. For example, one Neyrpic meter in ref. 7.3.4 was rated in three laboratories at the same towing tank temperature. The results were within

about 1 percent, i.e., + 0.5 percent about an average, for velocities between 1 and 11 ft

per second. However, at 0.5 ft per second this spread increased to more than 5 percent.

The only accommodation that can be made with this state of affairs, apart from trying to

avoid low-velocity measuring sections, is to consider these deviations when estimating the

total uncertainty of a measurement.

For errors caused by use of a group (rather than an individual) calibration, see sec- tion 7.4.1 above.

7.5.3. Boundary Effects

Ott and Neyrpic meters are apparently quite insensitive to wall and bottom proximity,

the effect generally being less than 0.5 percent even with the meter axis within one propeller diameter of the boundary (7.3.4, 7.6.4).

These results pertain only to geometric proximity effects at smooth walls and bottom.

A bottom roughened by large geometric features, e.g., dunes; will shed local vortices which

can cause meter registration errors. Therefore, close proximity to rough boundaries should

be avoided in spite of the data cited herein. See section 7.5.4.

7.5.4. Turbulence and Velocity Pulsation Errors

In general, propeller meters over-register because of longitudinal fluctuations and

under-register in the presence of transverse fluctuations. Natural turbulence includes

both fluctuations, but the effects do not necessarily compensate.

2 Re^erenge 7

. ^ . 5 .assigns to turbulence errors an upper limit of (0.5) (AV/V) with

AV=(u +v+w), where u, v and w are the turbulence fluctuations in three directions with respect to the time average velocity, V. If the turbulence intensity is 15

percent, there would be a velocity error (relative to a still-water calibration in a towing tank) not exceeding 1 percent, and the error would likely be negative. To give the

reader an example of one set of conditions which produce a 15 percent turbulence level,

approximately this intensity (in u^ alone) was measured by Jons son (7.6.7) near the bottom of a laboratory channel 4 ft wide and 0.5 ft deep which had been artificially roughened with transverse triangular ridges 0.5 cm high. McQuivey (7.6.8) lists turbulence

intensities found in several field situations. It is clearly important to select mea- suring stations where the turbulence is not obviously intense.

Velocity pulsations . In ref. 7.3.3 the effects of velocity fluctuations were observed

in a series of experiments in which Ott meters were oscillated both axially and transversely in flowing water. This type of experiment can be considered to approximate the effects of turbulence of low frequency and of a scale larger than the meter size.

The results can be described briefly as follows. For axial fluctuations, over-registration depended greatly on impeller geometry. For the same geometry it increased with

increasing amplitude of the fluctuation, with increasing frequency, with increasing rotor

inertia and with decreasing average velocity. The effect of transverse fluctuations depended mainly on meter geometry, but also increased slightly as the average velocity was re- duced. However, a propeller geometry could be selected (in this case, a three-bladed propeller with 5 cm pitch and 3 cm diameter) which was almost insensitive to transverse fluctuations over the range of variables covered in ref. 7.3.3, i.e., frequencies 2.6 to 10.5

Hz, average velocities 2 to 4 ft per second, and amplitudes of the velocity perturbations

from zero to the average velocity.

For the foregoing range of variables the errors for all the Ott propellers tested in

ref. 7.3.3 were generally less than 1 percent provided the amplitude of the velocity perturbation did not exceed 0.2 V. This result is in agreement with the upper limit criterion

cited in the second paragraph of this section (7.5.4).

55
7.5.5. Oblique Currents

Meters should be calibrated to check response to oblique approach flow, if this

information has not been supplied by the manufacturer and if accuracy is desired. Even

the so-called "component runners," which are intended to register only axial components,

deviate from this condition as the approach angle increases. For example, Neyrpic meters

tested by Johnson (7.3.4) indicated a 2.5 percent deviation at the high velocities for a

30° angle. However, for a 10° angle, the deviation was within 0.5 percent.

7.6. References

7.6.1. Buchanan, T. J. and W. P. Somers, "Discharge Measurements at Gaging Stations,"

Chapter A8, Book 3, of Techniques of Water Resources Investigations of the U. S. Geological Survey , 1969. U. S. Govt. Printing Office, Wash., D. C. 20402,

$0.70.

7.6.2. British Standards Institution, Standard No. 3680, "Methods of Measurement of

Liquid Flow in Open Channels: Part 3, Velocity Area Methods," 1964.

7.6.3. Coffin, J., "First Results Concerning the Effect of Water Temperature in the

Calibrating Tank," Paper A-3, Flow Measurements in Closed Conduits, H. M. Stationery Office, Edinburgh, U. K. , 1962.

7.6.4. Benini , G. , "Researches on Mutual Interference and Wall Proximity Effects on Current Meter Readings," Paper A-2, Flow Measurements in Closed Conduits, H. M. Stationery Office, Edinburgh, U. K. , 1962.

7.6.5. "Fluid Meters -- Their Theory and Application," Amer. Soc. Mech. Eng., 6th ed.,

1971.

7.6.6. O'Brien, M. P. and R. G. Folsom, "Notes on the Design of Current Meters," Trans.

Amer. Geophys. Union, 29, 2, Apr. 1948. (This reference was not included in the

General Information Sources, because it does not contain experimental information

directly useful in field applications. However, it is recommended for background

information because it presents in an easily followed style the analytical rationale behind propeller meter performance.)

7.6.7. Jonsson, I. G. , "On Turbulence in Open Channel Flow," Acta Polytechnica Scandinavica. No. Ci 31, 1965.

7.6.8. McQuivey, R. S., "Summary of Turbulence Data from Rivers, Conveyance Channels,

and Laboratory Flumes," U. S. Geol. Surv. Prof. Paper 802-B, 1973, U. S. Govt.

Printing Office, S/N 2401-02429, $1.55.

8. VELOCITY-AREA METHODS

8.1. Background

The velocity traverse is perhaps the most common field method for determining volumetric flowrate. It is also the most time-consuming method and is often unwieldy as well.

Nevertheless, it is resorted to in the following situations:

1. Streamgaging of rivers and large artificial waterways. In this application,

velocity traverses are often made upstream of a control point so that a stagedischarge relation for the stream can be established and periodically checked.

2. In small artificial free-surface conduits, including sewers, often for the

purpose of making a field calibration of a flume, weir or other measuring device.

3. In large closed conduits, often to determine flowrate through turbines for field

acceptance tests.

56
Procedures for the first application above, i.e., for streams and large artificial

channels which generally have large width-depth ratios and reasonably gradual depth changes,

are well established, and estimates of the errors involved are available, as in refs. 8.2.2

and 8.8.2. The third application has also received considerable attention, e.g., ref.

8.2.3. However, the second application can involve small rectangular sections of various

width-depth ratios or part-full circular conduits, both with non-uniform roughness distribution. Also, immersion of velocity measuring instruments is severely restricted in some types of wastewater. Therefore, procedures and error estimates for this application are not as well formulated as in the other cases. In this chapter, we call attention to possible error sources.

8.2. General Information Sources

8.2.1. Buchanan, T. J. and W. P. Somers, "Discharge Measurements at Gaging Stations,"

Book 3, Chap. A8 of Techniques of Water Resources Investigations of the U. S . Geological Survey, 1969. U. S. Govt. Printing Office, Wash., D. C. 20402.

$0.70. Cat. No. I19.15/5:bk3, Chap. A8, S/N 2401-0498.

This reference gives considerable detail on the use of current meters for

velocity traverses. In addition to covering the technical base for discharge

measurements, it is strong on descriptions of field equipment including cur- rent meters, cables and weights, winches, sounding equipment, etc.

8.2.2. I. S. 0. Standard No. 748, "Liquid Flow Measurement in Open Channels -- Velocity

Area Methods," 1973. Order from American National Standards Institute, 1430

Broadway, New York, N. Y. 10018. $12.95.

This document is particularly strong on estimation of errors associated with

the velocity measurements and with the various methods of velocity-area

traversing.

8.2.3. International Electrotechnical Commission, Publ. No. 41, "International Code for

the Field Acceptance Tests of Hydraulic Turbines," 1963. Order from American

National Standards Institute, 1430 Broadway, New York, N. Y. 10018. $36.00.

This code describes several methods for measuring flowrate in open and closed

conduits for turbine acceptance tests. The section on velocity-area current

meter procedure is written for propeller meters only.

8.2.4. "Water Measurement Manual," Bureau of Reclamation, U. S. Dept. Interior, Second

Ed., Revised Reprint, 1974, Chapters 5 and 8. United States Govt. Printing Office,

Wash., D. C. 20402. $5.80. Catalog No. 127 . 19/2 : W29/2 , S/N 2403-0027.

These two chapters give brief overviews on current-meter methods in open channels, although not with the detail of ref. 8.2.1, and of Pitot-tube traverses

in pressure conduits.

8.2.5. British Standards Institution, Standard No. 1042-2A, "Methods for the Measurement

of Fluid Flow in Pipes, Part 2: Pi tot Tubes -- 2A, Class A Accuracy," 1973.

Order from American National Standards Institute, 1430 Broadway, New York, N. Y. 10018. $13.00.

This standard gives details on Pitot-static tubes and on traversing procedures

which should result in an overall accuracy of 1 percent in pipe flow.

8.3. Errors in Streamgaging

8.3.1. Background

Streamgaging by velocity-area integration is normally accomplished by dividing the

stream into vertical strips and obtaining an "average" velocity within each strip by

57
measuring the velocity either (1) at many points throughout the depth (full profile), (2)

at 0.2 and 0.8 depth from the surface, or (3) at 0.6 depth from the surface. (The three

options were listed in order of decreasing accuracy.)

One method of estimating an overall measurement error is to use the square root of the sum of the squares of the error components. This was the method used in ref. 8.2.2 as is

shown in the following:

The overall random standard error in discharge, X , is (8.2.2)

QR - ^ + - (X? + + X^) [8.1] ^ mm ljdv

where: (1) X is the error associated with the number of vertical sections. Typical

values for a wide river with irregular bed profile are +5,3 and 1 percent

for 8, 15 and 50 vertical sections, respectively (8.2.2).

(2) X^ is the random error due to width measurement. This can be neglected if the

number of vertical sections is large.

(3) X is the random error due to depth measurement. This has to be estimated for

the individual case, as it clearly depends on the nature of the bottom, i.e.,

rigid or movable, the regularity of the bottom and the total depth.

(4) X is the average error of the mean velocity in all the verticals. It is

defined as

X = / 4 + X^ [8.2]

V V — o

where X^ is the standard deviation of a point measurement, p is the number of

points in a vertical, and X is the error associated with the number of points.

As a guide, X^ can be taken as 6 percent for 40-second readings (8.2.2).

Also, as a guide only, X can be taken as + 3.5, 3.0 and 0.5 percent for one- point (0.6 depth), two-point (0.2 and 0.8 depth) and full vrelocity profile

methods, respectively (8.2.2). These are values obtained from river gaging.

(5) m is the number of vertical sections.

Different values for the various error components can be found in ref. 8.8.2. Collection

of river flow data to improve these component error estimates is described in ref. 8.8.9.

In addition to the errors covered by eq. 8.1, systematic errors X _ must also be con- sidered. The major source here is the current meter calibration, and the error can usually be considered ' to be 1 percent at a maximum, provided very low velocity sections are avoided in accordance with the recommendation of refs. 8.2.1 and 8.2.2, and provided that

the meter is individually calibrated. The overall error X^ is then

8.3.2. Numerical Example

Consider a stream in which 10 vertical sections and the 0.2 - 0.8 depth method are used with 40-second velocity readings. From the foregoing we select X = 0.6, X = .03,

X^ = .01, X = .04, and a current meter error of 0.01. The overall standard error is then

computed to^e + 4.4 percent. Double this value, + 8.8 percent is the "tolerance," i.e.,

95 percent of the measured discharges will be within these limits. The greatest improvement would be brought about by increasing the number of vertical sections. If 50 sections

are used, the overall standard error is reduced to + 1.6 percent.

58
When conditions differ substantially from those for which the error component estimates of ref. 8.2.2 or 8.8.2 were made, users have to assign their own best estimate of errors

8.4. Errors in Small Conduit and Sewer Measurements

8.4.1. General

In this section we are concerned with flowrate measurements which are often made in a conduit in order to field check the performance of an open-channel metering device located

downstream. In these cases the X term of eq. 8.1 is not so meaningful, because there is

often little flexibility in the cffoice of number of vertical sections. Shallow flows often

preclude any procedure but the one-point method in any vertical. Durations of velocity

recording sometimes must be short to avoid fouling of the current meter. One element on

the positive side is that depth measurement errors should be minimal owing to the fixed

boundaries. In short, it is difficult to generalize limits of estimated errors and each

case should be considered individually.

In the following, we attempt to obtain rough estimates of the errors caused by obtaining only a few point velocities in a small conduit and by short sampling times at each

point

Suppose figure 8.1 represents the "true" velocity distribution in an approach channel

to a Parshall flume. The width is 4.0 ft, depth is 2.4 ft and 12 cfs are flowing, so the

average velocity is 1.25 ft per second, high enough for reliable current meter behavior.

Divide the section into four vertical strips 1 ft wide. Assume, for the moment, that

true point velocities are obtained. Then the two-point method (velocities measured at 0,2

and 0.8 depth) gives an average velocity 2.2 percent too high, an error which is due only

to the spatial distribution of the velocity sampling. If, additionally, we allow 1.0 percent for meter error and 6 percent error for short sampling time at each of the eight

points, the overall standard error is about + 3.2 percent and the "tolerance" is + 6.4

percent. The result could be improved most effectively by using more sampling points.

On the other hand, if the one-point (0.6 depth) method were used in each vertical

strip, the error in average velocity alone would be 5.0 percent in this example, and the

combined standard error would be + 5.9 percent.

Note that if this traverse were being made with a Price meter, the meter positions

would be just about at the allowable limits for wall proximity (see chapter 6). Therefore,

if this same velocity distribution were found in a channel half the size, 2.0 x 1.2 ft, and

only a Price meter were available, the one-depth method with two vertical sections would

have to be used, and the overall error would be close to + 10 percent. In this case, it

would probably be better to violate the wall proximity rules and use four vertical sections.

An alternative (not possible in sewage) would be to go to a Pygmy or propeller meter.

Table 8.1 summarizes the errors due to unrepresentative or incomplete spatial sampling

for the cross-sections of figures 8.1 and 8.2.

8.4.2. Numerical Example -- Rectangular Section

Table 8.1. Examples of Percentage Errors in Spatial Sampling

Flow No. of Verticals 0.6 Depth 0.2-0.8 Depth

Fig. 8.1a

Fig. 8.1a

Fig. 8.1b

Fig. 8.1b

4

24

2

+ 5.0 + 9.0

+4.5

+ 6.0

+2.2

+ 5.0

0 + 2.0

59
Figure 8.1. Example of velocity contours in a rectangular section.

(Avg. vel. = 1.23 ft/s)

1.43 ft/s

lo41

1.39 (avg.)

1.38

1.31

1.25

Figure 8.2. Examples of velocity contours in a part-full circular section.

60
The benefits of increasing the number of velocity measuring points are apparent. An

added benefit is that the error due to finite sampling time is, thereby, also reduced (eq.

8.2). This numerical example is presented only for illustration, in order to acquaint

users with the magnitude of errors that can be involved. It is not presented as a typical

situation. Many more representative flows would have to be investigated before these re- sults could be generalized.

Probably the most accurate traverse would result if one line of velocity points were

taken with a propeller meter as close as permitted to the walls and bottom, with the interior points of the traverse spread accordingly. Then the flowrate could be determined

graphically as recommended for closed conduits, e.g., ref. 8.2.3, with the velocity distribution between the boundaries and the outermost velocity points being estimated by an appropriate power law curve.

8.4.3. Numerical Example -- Circular Section

The sketches of figure 8.2 represent velocity contours obtained in a smooth laboratory pipe at Reynolds numbers of approximately 10 (8.8.7). They could also represent con- tours for larger, rougher pipes at higher Reynolds numbers.

In the case of larger sewers where access is only available from street level through

a manhole, for practical purposes current meter measurements are obtainable only along the

vertical centerline. In the shallow-flow cases of figure 8.2a, a single measurement at

0.6 depth will record (if registration of true velocities is assumed for this discussion)

a velocity about 5 percent less than the average velocity. Using the 0.2 and 0.8 depth

method improves this to about a 3 percent error.

When the pipe flows half-full (figure 8.2b) the error is about 3.3 percent for both

the one-point method and the two-point method.

Caution : The errors in the foregoing appear deceptively small. Users are cautioned

that the data available on velocity distribution are extremely limited for part-full flow

in pipes, so that figure 8.2 is not necessarily representative. Also, the distribution will

change with Reynolds number and roughness.

8.4.4. Error Due to Finite Sampling Time

The errors due to finite sampling time at a point as given in refs. 8.2.1 and 8.8.2 were obtained from numerous measurements in rivers and are not necessarily valid for small

channels and sewers.

The following equation for estimating sampling time on the basis of turbulence parameters is given in ref. 8.8.5.

t = 2uh /xl [8.4]

X f

Here t is the measuring time (seconds), u is the r.m.s. turbulence level, T is the macro

time scale of the turbulence, and is the sampling time error as in eq. 8.2. We assume

that T = L /V, where V is the average velocity and where L is the turbulence macro scale,

which we can further assume to be of the order of the depth of flow (sometimes the width is

used)

Then, in the first illustration of section 8.4.2, if we want to attain = 0.06 at

each sampling point, and if we assume that the flow is fairly smooth with a turbulence

level of 10 percent (see section 7.5.4), then the required sampling time is about 13 sec- onds .

8.5. Floats

The use of floats is actually a rudimentary velocity-area procedure and is, therefore,

discussed in this chapter. Factors for multiplying float velocities to obtain average

velocities according to ref. 8.8.1 are given in the curves of figure 8.3 for floats of

61
various vertical lengths. These factors really refer to individual vertical strips of a wide section rather than to relatively narrow rectangular channels. For example, applying

these factors to a centerline surface float in figure 8.1a gives an average velocity 5 percent too high, while use of two vertical strips yields an average velocity about 7 percent

too low. A value of n = 7 was used in this illustration. Similarly, centerline surface

floats in part-full circular sections of figure 8.2 in conjunction with figure 8.3 give

average velocities about 10 percent too low.

The table of coefficients in figure 8.3 is intended for large dish-shaped sections

where only a centerline surface float measurement is available. If several float measurements are made across the section, the coefficients from the curve of figure 8.3 should be

used.

8.6 . Optical Current Meter

The optical current meter developed by the U. S. Geological Survey (refs. 8.2.1,

8.8.3, 8.8.4) should be mentioned along with surface floats, since it obtains a surface

velocity measurement by "stopping" the surface motion with a rotating prism arrangement.

It was developed for use in heavily debris-laden flows, which would be destructive to

intrusive meters. Limitations on its use are discussed in ref. 8.8.4.

8.7. Closed (Pressure) Conduits

The use of velocity-area methods in closed conduits has been well-documented in refs.

8.2.3 and 8.8.6 and will not be discussed in detail here. Both current meters and Pitot

tubes can be used in this application. The largest uncertainty is associated with the

blockage effect of current meter arrays. This effect has not been fully evaluated yet, but

the most recent developments are summarized in ref. 8.8.8. The Pitot tube .method is capable of good accuracy if done according to recommendations. Reference 8.2.5 is the most

complete source of information on this method.

8.8. References

8.8.1. British Standards Institution, Standard No. 3680-3, "Methods of Measurement of

Liquid Flow in Open Channels: Part 3, Velocity Area Methods," 1964.

8.8.2. Carter, R. W. and I. E. Anderson, "Accuracy of Current Meter Measurements," Proc.

Amer. Soc. Civ. Eng., 89, HY4, July 1963, 105-115.

8.8.3. Chandler, T. S., and W. Smith, "Optical Current Meter Use in Southern California,"

Proc. Amer. Soc. Civ. Eng., £7, HY9 , Sept. 1971, 1461-69.

8.8.4. Smith, W. , and G. F. Bailey, "Optical Current Meter," Proc. Amer. Soc. Civ. Eng.,

88, HY5, Sept. 1962, 13-22.

8.8.5. Jonsson, I. G. , "On Turbulence in Open Channel Flow," Acta Polytechnica Scandinavica, No. Ci 31, 1965.

8.8.6. International Standards Organization, "Draft Proposal for an ISO Standard: Measurement of Clean Water Flow in Closed Conduits by the Velocity Area Method Using

Current Meters," ISO/TC 30/SC3:67E, 1972.

8.8.7. Nalluri, C. and P. Novak, "Turbulence Characteristics in a Smooth Open Channel of

Circular Cross -Section , " Jour. Hydraulic Res., ]A, 4, 1973, pp. 343-368.

8.8.8. Kinghorn, F. C, "Twelfth Meeting of the International Current Meter Group," Water

Power, Nov. 1973, pp. 432-435.

8.8.9. I.S.O. Standard No. 1088, "Liquid Flow Measurement in Open Channels, VelocityArea Methods, Collection of Data for Determination of Errors in Measurement," 1973,

ANSI. $7.70.

62
1

0

— L..Q_^ Rat

1 1

io of float

1

height to flow depth

1:21 —

—

0.25

^^Surface

4 5 6 7 8

Value of n ^ ^

(*) Float velocities are multiplied by this

factor to obtain average velocity in a vertical strip.

(**) Exponent in power law velocity profile:

v/Vs= ( y/D

where v is velocity at elevation y, D is

depth of vertical strip, and is surface

velocity, n = 7 corresponds to a smooth

bed and n = 5 to a rough bed, approximately.

Coefficients to Apply

Surface Velocity of D

to Obtain Avera;

Avg. Depth in

reach, ft.

to Centerline

sh-shaped Sections

;e Velocity

Coefficient

12

3

5

9 15

>20

0.66

0.68

0.70

0.74

0.77

0.79

0.80

Figure 8.3. Surface float coefficients, from ref. 8.8.1.

63
9. CHEMICAL ADDITION METHODS

9.1. Introduction

Chemical addition techniques for volumetric flowrate measurement include "tracer"

procedures, e.g., the salt-velocity method, and dilution methods. The latter can be based

on the color, conductivity, fluorescence (and sometimes radioactivity) of the material

injected into the flow.

These methods have in common requirements for specialized equipment, scrupulous care

and often considerable time for their execution. They are therefore likely to be expensive

in terms of instruments, special setups and labor, particularly when compared with current

meter traverses. On the other hand there are situations -- small but highly turbulent

streams and raw sewage flows, for example -- where current meters are often impractical

but chemical methods are useful. For that reason, and also because of their potential for

high accuracy, the dilution methods comprise an important flow measurement tool, both for

direct streamgaging and for in situ calibration of flowrate measuring devices.

9.2. General Information Sources

9.2.1. International Electrotechnical Commission, Publ. No. 41, "International Code for

the Field Acceptance Tests of Hydraulic Turbines," 1963. Order from American

National Standards Institute, 1430 Broadway, New York, N. Y. 10018. $36.00.

This code gives considerable detail on the salt-velocity test, including

features of the salt tank, pop valves, injection arrangement and electrodes.

9.2.2. I. S. 0. Standard No. 2975/1, "Measurement of Water Flow in Closed Conduits

Tracer Methods--Part I: General," 1974. Order from American National Standards

Institute, 1430 Broadway, New York, N. Y. 10018. $7.90.

This is the first of a projected series of seven I. S. 0. standards on tracer

methods in closed conduits. Advantages and disadvantages of the chemical addition methods and of the various tracers are listed in this introductory

document. Information on necessary mixing lengths and on estimating errors is

also given.

9.2.3. I. S. 0. Standard No. 555, "Liquid Flow Measurement in Open Channels Constant

Rate Injection Method," 1966. Order from American National Standards Institute,

1430 Broadway, New York, N. Y. 10018. $10.15.

This standard given details on colorimetric , conductivimetric and volumetric

chemical analysis methods of dilution analysis, as well as site and injection

equipment requirements for the constant rate dilution method. Examples of error estimation are also given.

9.2.4. "Fluid Meters -- Their Theory and Application," Amer. Soc. Mech. Eng., 6th ed.,

1971, Chapter I-O, Order from ASME, 345 E. 47th St., New York, N. Y. 10017.

$20.00. ($16.00 to ASME members).

Details on the salt-velocity method and brief overviews of other methods.

9.2.5. Replogle, J. A., L. E. Meyers and K. J. Brust, "Flow Measurements With Fluorescent

Tracers," Proc. ASCE, 92_, HY5, pp. 1-15, Sept. 1966. Also see discussion of this

paper by F. A. Kilpatrick, W. W. Sayre and E. V. Richardson, Proc. ASCE, 93, HY4,

pp. 298-308, July 1967. Obtain from Engineering Societies Library, 345 E. 47th

St., New York, N. Y. 10017. $0.25 per page plus $3.00 for each volume handled.

These papers, in addition to covering the principles of the methods and the

comparative advantages of continuous vs. slug injection, give some details

on the handling of equipment and tracers.

64
9.2o6. Blakey, A. W. , "Flow Measurement in Sewers Using a Constant Rate of Injection Dilution Technique," Jour. Inst. Municipal Engrs., 96, Feb. 1969, pp. 44-52. Obtain

from Engineering Societies Library, 345 E. 47th St., New York, N. Y, 10017.

$0.25 per page plus $3.00.

Lithium chloride was used as the additive in these measurements. However,

the interest in this paper lies in the detail with which the sewer measurement planning, operation and costs are described.

9.3. Salt Velocity Method

In the salt velocity method, brine is injected suddenly at an upstream station in

such a manner that it becomes well distributed across the section very rapidly. The time

of passage of the salt pulse between two downstream stations is measured by means of electrodes which detect the increased conductivity associated with the passage of the brine.

The flowrate can then be determined provided that the volume of the conduit between the

electrode stations is accurately known.

The salt velocity method has a potential for better than 1 percent accuracy when

properly used. Major error sources are improper determination of elapsed time between the

centers of gravity of the recorded conductivity pulses and inaccurate determination of con- duit volume.

References 9.2.1 and 9.2,4 are recommended for information on this method. Although

these documents are mainly written and illustrated in terms of circular closed conduits,

the procedures can be adapted to open channel flows. Because velocities in open conduits

are often low, users are cautioned to note the minimum velocity vs. brine-density criteria

cited in ref. 9.2.1.

The method as described in ref. 9.2.1 and elsewhere requires an array of injection

points at the upstream injection station, and an array of immersed electrodes at the downstream stations. Therefore, it would have to be used with caution in raw domestic sewage.

Lengths of regular conduit geometry are desirable for this test.

In some situations it is possible to obtain an average velocity between stations by

visually determining the time of passage of a dye cloud (9.5.9). This method could be

refined by using fluorometry to determine time of passage.

9.4. Dilution Methods

Dilution methods can employ either constant rate (continuous) injection (9.2.3) or slug injection. The progressive dye dilution is shown in figure 9.1 for the two methods

as illustrated in ref. 9.2.5. Accuracy in both cases depends, among other factors, on adequate lateral mixing at the sampling station and on accurate concentration measurement.

Dilution methods are further subdivided by the type of material or dye added and/or by the

property which is analyzed to determine the dilution. These are briefly mentioned in the

following paragraphs with references to the best available literature on the subject.

9.4.1. Constant Rate Injection

The basic principle of the constant rate method is expressed in the following continuity equation

Q = q(C^ - C^)KC^ - Cq) [9.1]

where Q is the flowrate to be measured, q is the injected constant flowrate of additive

concentration C , C^ is the concentration at the sampling station, and Cq is the background

concentration or the particular additive in the water. The main advantages of this method

are that the sampling can be done during a concentration plateau (figure 9.1) and that the

long injection period reduces the adverse effect of slack water areas in natural streams

(9.5.3). It is also more suitable for unsteady (time varying) flow than is slug injection.

65
9.4.2. Constant Rate Injection -- Error Sources

Equation [9.1] assumes that no dye is lost between injection and sampling stations by

either physical or chemical action. See refs. 9.2.2, 9.2.5 and 9.5.2 for comments on dye

stability. Any dye loss will be reflected as apparent additional dilution and hence apparent greater flowrate. For example, in sewer measurements it is important to stay upstream of chlorination stations (9.5.1).

The main disadvantage of this method is shown in eq. 9.1, namely that the injection

rate has to be accurately measured as well as the injected concentration C^^. Errors in

measuring are also important but are common (to varying degrees) to all dilution methods .

9.4.3. Length Required for Transverse Mixing

Another error source common to all dilution methods is failure to achieve sufficient

lateral mixing at the sampling station. Several criteria are available, e.g., refs. 9.2.2,

9.2.5 and 9.5.3, but this factor is still in doubt. It is best to be conservative in

length, but to check to be certain that the length is not so great as to cause dye loss.

As a numerical example, consider an 8-ft diameter trunk sewer flowing half full on a slope of 0.00020 with an average velocity of 3 ft per second. Most criteria for mixing

length have been developed for rivers or wide, shallow canals. Nevertheless, using the

100 X top width criterion of ref. 9.2.5 results in an 800 ft required length. Using a rationally based criterion of ref. 9.5.3, the required distance is about 480 ft. Adapting

the closed-conduit recommendation of ref. 9.2.2, the measuring length should be about 1000

ft for the concentration across measuring section to be within one percent of uniform. To

be conservative, one is inclined to select the largest distance (or the closest manhole

spacing increment) provided one can find such a length without sewer junctions.

9.4.4. Slug Injection

The principle of the slug injection method is expressed by the equation

qJ(C2 - C^)dt = C^(Vol.) [9.2]

where t is time, (Vol.) is the volume of the injected slug of dye, and Q, Cq, and and

are as defined earlier.

It is clear from eq. 9.2 that the main disadvantage of this method is that the tracer wave has to be sampled over its entire time of passage. See figure 9.1. (The previous

requirement for adequate lateral mixing of course still prevails.) On the other hand, the

main advantage (relative to constant rate injection) is that the injection apparatus need

not be so sophisticated, since only the total injection load of the dye need be known ac- curately. Slug injection is best-suited for regular, artificial conduits, because they

have no slack water areas to entrap or delay dye.

References 9.2.5 and 9.5.7 give additional information on the slug injection method.

9.4.5. Slug Injection -- Error Sources

As is the case for constant rate injection, there can be no dye loss between injection

and sampling, and dilution analysis must be carefully made. Additionally, the observer

must be careful that the entire dye pulse at the measuring station is sampled. Failure to

do this always results in too high a flowrate determination.

9.4.6. Selection of Additive

Florescent dyes have been studied in detail by the U. S. Geological Survey (9.5.2).

Rhodamine WT dye has shown extremely small dye loss to channel boundaries and sediment and

is therefore recommended for dilution studies. It has been used successfully in raw sew- age flows (9.5.1). Existing fluorometers properly used appear to be capable of 1 percent

accuracy

.

66
Channel banks or walls

Flow^

Distance

a. Spatial distribution of tracer in slug injection.

Flow

b

Distance ^

b., Spatial distribution of tracer in continuous injection.

uu

a

u

a

oo

Time

c. Time-concentration curves in slug injection.

Sample plateau

Time

d. Time-concentration curves in continuous injection.

Figure 9.1. Dye dispersion for slug injection and constant rate

of injection, after Kilpatrick, et al., (9.2.5).

67
Sodium dichromate is the most common dye used when dilution is measured by colorimetric analysis. Accuracy of colorimetric analysis can be seriously affected by suspended

matter in the flow or by chromium ions in wastewater (9.2.3), Sodium chloride is frequently

used when the dilution determination is to be based on conductivity. Large quantities

might be required for continuous injection, particularly if the background level of salt in

the flow is high. Minimum concentrations for 1 percent accuracy of analysis are given in

ref. 9.2.3.

Details on analysis by colorimetry and conductivity as well as chemical analysis by

titration are given in ref, 9.2.3, All three methods are potentially capable of 1 percent

accuracy. See ref. 9.2.5 for some details on fluorometric analysis.

Lithium chloride is apparently used frequently in the U. K, , with analysis by flame

photometry (9.2.6).

9.4.7. Radioisotope Methods

The use of radioisotopes for dilution discharge measurements has been studied extensively by the U, S, Bureau of Reclamation in collaboration with the U, S, Atomic Energy

Commission (9.5.4, 9,5.5). The counting procedures used for dilution analysis here are more accurate than the fluorometric, colorimetric or conductivity analyses of the previous

sections. Although the dosages required for discharge measurements are well below accepted

safety limits, radioisotope use in flow measurement has been handicapped by handling problems and by general public apprehension (9.5.2), It is therefore unlikely that its use will ever become widespread in local water and sewerage districts in spite of its potential

for high accuracy. It is not further discussed here, but interested readers can note that

a British standard is available for this method (9,5.6).

9,4.8. Overall Accuracy

It is difficult to pinpoint from available information the overall accuracy of care- fully made dilution discharge measurements. In ref. 9.5.1 Kilpatrick achieved slightly

better than + 2 percent with continuous injection in the laboratory (although for only two

tests). It can be assumed that similar accuracy could be attained in artificial conduits

under good conditions in the field, with somewhat poorer accuracy achievable in natural

streams. The same accuracy would be achievable in dilution tests using colorimetry, con- ductivity and volumetric titration, provided that the respective analyses were made with

the same degree of accuracy as fluorometric analyses.

Note that the capability for this accuracy makes dilution methods suitable for in situ

calibration of flowmeters which are not usually accurate to 2 percent uncalibrated . This

is particularly true, for example, for Parshall flumes, which are usually considered + 3 to 5 percent instruments under the best of circumstances. However, for the procedure used

in ref. 9.2.5, accuracies of only 3 to 5 percent were claimed.

9.5. References

9.5.1. Kilpatrick, F. A., "Flow Calibration by Dye-Dilution Measurement," Civ. Eng.,

Feb. 1968, 74-76.

9.5.2. Wilson, J, F,, "Fluorometric" Procedures for Dye Tracing," Chap. A 12, Book 3 of

Techniques of Water-Resources Investigations of the U, S, Geological Survey , 1968,

(Out of print at U, S, Govt, Printing Office),

9.5.3. Discussion of ref. 9.2.5 by Fischer, H. B. , Proc. Amer. Soc. Civ. Eng., 93, HYl,

Jan. 1967, 139-140.

9.5.4. Schuster, J. C, "Canal Discharge Measurements with Radioisotopes," Proc. Amer.

Soc. Civ. Eng., ^I, HY2 , March 1965, 101-124.

9.5.5. Schuster, J. S. and Hansen, R. L., "Radioisotopes and Turbine Flow Measurements,"

Proc. Amer. Soc. Civ. Eng., 98, POl, June 1972, 1-9.

68
9.5.6. British Standard No. 3680-2C, "Methods of Measurement of Liquid Flow in Open Channels, Part 2: Dilution Methods -- C. Radioisotope Techniques," 1967. British

Standards Institution (British standards are distributed in the U. S. by the American National Standards Institute, 1430 Broadway, New York, N. Y. 10018).

9.5.7. Kilpatrick, F. A., "Dosage Requirements for Slug Injections of Rhodamine BA and WT

Dyes," U. S. Geol. Survey Prof. Paper 700-B, in Geological Survey Research, 1970.

9.5.8. "Water Measurement Manual," Bureau of Reclamation, U. S. Dept. of Interior, Second

Ed., Revised Reprint, 1974. See p. 164. See ref. 2.3.1 for ordering information.

Table 9.1

Tabular Summary of Chemical Addition Methods

Application /Property

Streamgaging

Open conduits (canals)

Sewers

Unsteady flow

Silty water

Accuracy (potential)

Cost/Labor

Calibration of

other devices

Salt Velocity

Not suitable

(9.2.1)

Suitable, regular

planform conduits

only (9.5.4)

Suitable with

caution

Not suitable

Suitable

High (1 percent)

High

Suitable

Dilution

Suitable, continuous

injection only (9.5.3)

Suitable

Suitable with caution

Suitable, continuous

injection only (9.2.5)

Suitable with caution

Good (2 percent)

High

Suitable (9.5.1)

10. OTHER OPEN CHANNEL METHODS

10.1. Introduction

This chapter covers a few additional open channel methods which did not appear to

belong in the previous chapters. In general, these methods are not as accurate as the

traditional methods already described.

10.2. Submerged Orifice

10.2.1. Introduction

The submerged orifice (see figure 10.1) is a rectangular opening which can either have

contractions on all four sides or have the contractions suppressed on the bottom and/or

sides. In this respect, it is analogous to the thin-plate weirs (chapter 4). Unfortunately,

the data base for submerged orifices does not appear to be as complete as that for the

weirs

Although the submerged orifice is used mainly for irrigation flows, it could also be

used in specific situations in wastewater flows. The suppressed-contraction form would be

required to pass solids, and only flows providing self -cleansing upstream velocities (after

installation of the obstruction) could be considered.

69
RECOMMENDED DIMENSIONS

D L B A E W C

(ins) (ins) (ft) (ft) (ft) (ft) (ft)

3 12 4.0 10.0 3.0 2.5 2.0

3 24 4.0 12.0 3.0 3.5 2.0

6 12 5.0 12.0 3.5 2.5 3.0

6 18 5.0 14.0 3.5 3.0 3.0

6 24 5.0 14.0 3.5 3.5 3.0

9 16 6.0 14.0 3.5 3.0 3.0

9 24 6.0 16.0 3.5 3,5 3.0

Figure 10.1. Submerged orifice structure, from ref. 10.2.2.1.

70
The equation for discharge through a fully contracted (distances from orifice edges

to stream boundaries greater than twice the least dimension of the orifice) submerged

orifice is

Q= 0.61A[2g(H + h)]^^^ [10.1]

3 2 where Q is the flowrate in ft Is, g is the acceleration due to gravity (32.2 ft per sec ),

A is the area of the orifice in ft^, H is the difference between water surface elevations

upstream and downstream of the orifice, in ft, and h is the approach velocity head, V /2g,

in ft, based on the average upstream velocity, V. No published data are available on the

reliability of the coefficient, 0.61, but it appears to be consistent with the (circular)

orifice coefficients of chapter 11. It also follows that edge sharpness must be maintained

for the coefficient to remain valid.

If the bottom and/or sidewall contractions are suppressed (see figure 10.1), eq. 10.1 can be replaced with

Q = 0.61(1 + 0.15r)A[2g(H + h)]^''^ [10.2]

where r is the ratio of the suppressed part of the orifice perimeter to the total perimeter.

According to ref. 10.2.2.1, eq. 10.2 is approximate, but no quantitative information on its

accuracy is available.

10.2.2. General Information Sources

10.2.2.1. "Water Measurement Manual," Bureau of Reclamation, U. S. Dept. of the Interior,

Second Ed., Revised Reprint, 1974. Order from U. S. Government Printing Office,

Wash., D. C. 20402. $5.80. Cat. No. 127 . 19/2 :W29/2 , S/N 2403-0027.

This reference gives solutions to eqs. 10.1 and 10.2 in tabular form.

Recommended sizes of inlet sections are given, along with information on combination regulating/measuring devices for use at irrigation turnouts.

10.3. Free Overfall

10.3.1. Background

When an open channel discharges with a free fall in air, as in figure 10.2, the ratio

of the brink depth, y , to the critical depth, y , is a function of channel shape, slope

and roughness. Becaule critical depth can be refated to flowrate, brink depth can be used

as a measure of flowrate.

For example, some experimental results for y /y as a function of channel slope-tocritical slope ratio, S /S , are shown in figure for rectangular channels. In rec- tangular channels, according to the principles of critical flow

Q= Bg^V^^

where B is the channel width. Consider a channel at zero slope. Using y /y = 0.715 from

figure 10.3,

Q = 1.654 Bg^'''^y (Horizontal rect. channel) [l0.4]

e

If the channel is sloped, a trial procedure must be used, since we cannot know y /y^

from figure 10.3 without knowing S /S . But S in turn cannot be computed (from Manning's

o c c equation, see eq. 10.5) without knowing Q to begin with. One procedure for small slopes is as follows.

The slope and y are measured

e

(a) Use eq. 10.3 or 10.4 to estimate Q from measured y , i.e., use y^/y^ = 0.715 as

a first approximation.

71
(hydrostatic

critical depth) T

I'

Figure 10.2. Free overfall into atmosphere.

0.8

0.7

o 0.6

0)

0.5

0.4

-10

1- ^^^^>

-1- Ref . 10.3. 2.2

; X Ref . 10. 7.1

\\

\ ^ A ^

> \

\ \

V \ \

> ^

-5 0

s /s

o c

10 15

Figure 10.3. Rectangular free overfall data.

72
(b) Use this Q and corresponding y to determine S from the Manning equation, and

then S /S . ^

^ o c

(c) Using the second approximation value of y from step (c), get second approximation Q from eq. 10.3, and repeat procedure until convergence.

For circular channels the relations are more complex. An experimental Q vs . y curve

is given in figure 10.4 from ref. 10.3.2.1 for horizontal channels only. Also, from ref.

10.3.2.1, curves are reproduced in figure 10.5 for sloping channels to obviate the need for

the foregoing successive-approximation procedure.

Caution . The data for circular channels from ref, 10.3.2.1 are based on experiments

on one pipe size only (8 inches), and should be treated cautiously until corroborating

data are available.

Caution. Because the high curvature of the flow will cause stilling wells to give erroneous results at and near the brink, y can be measured only by some type of surface

probe

.

The ratio y /y has been found to be essentially unaffected by modest increases in

channel roughness, e.g., ref. 10.3.2.2.

10.3.2. General Information Sources

Rajaratnam, N. and Muralidhar, D. , "End Depth for Circular Channels," Proc

.

Amer. Soc. Civ. Eng., 90, HY4, March 1964, pp. 99-119. Order from Engineering

Societies Library, 345 E. 47th St., New York, N. Y. 10017. $0.25 per page plus

$3.00.

Delleur, J. W. , Dooge, J. C. I., and Gent, K. W. , "Influence of Slope and

Roughness on the Free Overfall," Proc. Amer. Soc. Civil Eng., 82, HY4, Aug. 1956,

pp. 1038-30 to 1038-35. Order as above.

These references give basic analysis and experiments on the free overfall.

However, they are concerned with the mechanics of the overfall and not

primarily with the overfall as a measuring device.

10.3.3. Error Sources and Comments

The foregoing results are valid only for free discharge such that the nappe is sur- rounded by atmospheric pressure. In a rectangular overfall with the sidewalls continued

past the brink, sub-atmospheric pressures reduce the average pressure in the nappe at the

brink section and consequently reduce y^/y •

An example of the effect of reduced pressure is shown in figure 10.6 from ref.

10.7.2. In this case, an abrupt slope change is being used as an overfall. The difference in y /y from the completely free discharge case is about -10 percent for this ex- ample, corresponding to an error in Q of -15 percent.

Even if the lower nappe of a rectangular overfall is aerated, the presence of ex- tended sidewalls can modify y /y slightly from the completely free case. With sidewalls

present y /y = 0.715 is a generally accepted value for the horizontal rectangular channel. If there are no sidewalls to restrain the nappe, y /y is probably reduced by about

1 percent.

A survey of available experimental results on the horizontal rectangular overfall

suggests that the value y /y = 0.715 should probably be assigned an accuracy of about +

3 percent. Also, problem! iS measuring the depth of water that is moving rapidly and in a curved path along with increased uncertainty in y /y for slopes combine to make the overfall method less accurate in general than weir or flume methods.

73
0.8

0.6

0.4

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Q/(g^/V/2)

Figure 10.4. Discharge vs. brink depth for horizontal circular channels, from ref. 10.3.2.1.

0.8

0.6

0.4

0.2

-40

I 1 n = Manning n

v^O.8''

oT6^

^0.4

0.2 - -0.1

-0 . 05

iP.Ol

-20 0 20

<l/3 / 2

40

4.42 Sy7n g

60

Figure 10.5. Discharge of sloping circular channels with free

overfall, from ref. 10.3.2.1. Abscissa ft-lb-sec

units only.

Water surface for discharge

Figure 10,6. Effect of sub-atmospheric pressures beneath overf

74
There is insufficient data to permit assessment of the accuracy of the circular overfall information.

10.4. Acoustic Flowmeters

Acoustic meters can be applied to open channels and users are referred to section

11.12.

10.5. Slope-Area Method

In the slope-area method, the depth is measured, preferably in a long reach of uniform

flow, and the Manning equation is used to estimate the flowrate. The Manning equation is

2/3 1/2

Q = (1.49/n)AR '-"s [l0.5]

where A is the sectional area of flow, R is the hydraulic radius, S is the bottom (and

water surface) slope in uniform flow, and n is an empirical roughness coefficient. The

numerical coefficient in eq. 10.5 is valid for foot-second units only. Estimated values of n for various types of channels can be found in most hydraulic textbooks and handbooks,

e.g., ref. 2.8.1. Area and hydraulic radius can be determined from the depth measurement

for known channel shapes. The slope can be measured, but it will be correct for use in eq.

10.5 only to the extent that the flow is close to uniform. By far the largest uncertainty

in this method is due to the estimate of the Manning n. Unless there is some independent

method for determining this coefficient (including the possibility of its variability with

depth), this method has to be regarded as an estimate only. See ref. 10.2.2.1.

10.6. Other Methods

Other methods and devices for open channel flowrate measurements, such as deflection

meters, propeller meters and others, can be found in ref. 10.2.2.1. Some indirect methods

for determining peak streamflow are described in refs. 10.7.3, 10.7.4 and 10.7.5.

10.7. References

10.7.1. Rajaratnam, N. and Muralidhar, D. , "Characteristics of the Rectangular Free Overfall," Jour. Hydraul. Res., 6, 3, 1968, pp. 233-258.

10.7.2. Rouse, H. , "The Distribution of Hydraulic Energy in Weir Flow with Relation to

Spillway Design," M. S. Thesis, M.I.T., 1932.

10.7.3. Bodhaine, G. L. , "Measurement of Peak Discharge at Culverts by Indirect Methods,"

Book 3, Ch. A3 of Techniques of Water-Resources Investigations of the U. S. Geological Survey , 1968.

10.7.4. Matthai, H. F., "Measurement of Peak Discharge at Width Contractions by Indirect

Methods," Book 3, Ch. A4 of Techniques of Water-Resources Investigations of the

U. S. Geological Survey , 1967.

10.7.5. Hulsing, H. , "Measurement of Peak Discharge at Dams by Indirect Methods," Book 3,

Ch. A5 of Techniques of Water-Resources Investigations of the U. S. Geological

Survey , 1967.

11. INSTRUMENTS AND METHODS FOR CLOSED CONDUIT FLOWS

11.1. Introduction

Three flow measurement methods used in closed conduits, i.e., the salt-velocity method,

dilution techniques, and velocity-area integrations were covered separately in chapters 8

and 9. The scope of instruments and methods covered in this chapter ranges from rudimentary (and often inexact) methods for situations where approximate and ad hoc measurements

are needed, through the traditional differential-head meters, to sophisticated modern

meters based on magnetic or sonic principles. Instruments and methods will be taken up in

the following sections in approximately increasing order of sophistication.

75
11.2. Trajectory Method (Purdue)

11.2.1. Background

If flow discharges into air from the end of a horizontal pipe, the flowrate can be

determined from trajectory measurements as shown in figure 11.1. This is a situation frequently encountered in industrial wastewater outfalls. The trajectory measurements are used in conjunction with curves derived from Purdue University experiments in 1928 on pipes 2, 3, 4, 5 and 6 inches in diameter. See figure 11.2. Note that this method can be

used for part-full pipe discharge (use the curves for X = 0) provided the brink depth is

less than 0.8 diameter.

11.2.2. General Information Sources

11.2.2.1. "Water Measurement Manual," Bureau of Reclamation, U. S. Dept. of the Interior,

Second Ed., revised reprint, 1974, Ch . 8, pp. 199-203. U. S. Govt. Printing

Office, Washington, D. C. 20402. $5.80. Cat. No. 127 . 19/2 : W29/2

,

S/N 2403-0027.

11.2.3. Comments

The results of using figure 11.2 will not agree with results obtained analytically by

treating the issuing water as a freely falling body, as described in section 11,4. Be- cause figure 11.2 is based on experiment, its use is recommended over the use of the theoretical parabolic trajectory, eq. 11.2, when standard commercial steel pipe (of the sizes

covered in figure 11.2) is involved.

11.3. California Pipe Method

11.3.1. Background

The California Pipe Method involves the measurement of the overfall depth at the end

of a short length of horizontal pipe flowing part full. See figure 11.3. It is a closed

conduit method only to the extent that part-full flow can be achieved in the horizontal

stub. The discharge, Q, in cubic feet per second is given by

Q = 8.69(1 - a/d)^-^^ d^'^^ [11.1]

where a is the distance in feet from the inside top of the pipe to the water surface, mea- sured at the end section (figure 11.3), and d is the inside diameter of the pipe in feet.

It is recommended that a/d be restricted to values greater than 0.5. The experiments from

which eq. 11.1 is derived used pipe diameters from 3 to 10 inches.

11.3.2. General Information Source

11.3.2.1. "Water Measurement Manual," see (11.2.2.1) for ordering information. See Ch. 8,

pp. 196-198 for California Pipe Method.

11.3.3. Comments

The California Pipe Method is related to the free overfall method of flow estimation,

which is really an open channel method and which has more general application. See chapter 10.

The Purdue trajectory method, with X = 0 (see figure 11.1), should be approximately

comparable to the California Pipe Method when the pipe is part full, and it is interesting

to compare the results for two typical cases.

Case 1 : 6-in. pipe, depth at end section is 3 inches. Using trajectory data

(11.2.1), flow is 200 gpm. Using eq. 11.1 and converting to gpm, flow is 190

gpm, a difference of about 5 percent.

76
X

c

1

.1111 1 1 1 K 1 1 M \ \

1 \ 1 \ 1 \ \

l\ 1 l\l

\ V1 \ \

\

\ \

\ \

\ \ \ \ \ \ \

\ \

\

\

\

— X = 18 inches ~ X = 12 Inches

1 1 1 1 1 1

Inside diame;ter = 2 iir 4 inJrk.____^

b \ \

\

V, N \

1 1 1 1 1 1

1 1

\

\

\

\ 1 1 I 1

\ \

\ \

\ * -

^ 1

5 10 20 50 100 200 500 1000 2000

w

<u J

Xioc

•1-1

- 1 1 1

1

1

1

1 1 1 1 1 1 1 1 1 1 1

\

~ X = 6 inches \

>. _ X ^ 0 inches \ \

\

\ \

-—

\

\

\

\ x \

\ \

\ \ \

\ \ \ \ \ Inside diameter^ 2 in- . 4 in- \ \ 6 in\

\ \

1 1 1 1

1 1

. i\ 1 1 ^ 1 1 M 1 1

10 20 50 100 200

Flow, gallons per minute

500 1000 2000

Figure 11.2. Discharge data for Purdue trajectory method,

from ref. 11.2.2.1.

77

1
Case 2 : 6-in. pipe, depth at end section is 2 inches. Using trajectory data

(11.2.2), flow is 110 gpm. Using eq. 11.1, flow is 88 gpm. (The end depth method

of chapter 10 gives 95 gpm.)

Some of this difference is caused by comparing exact 6-inch diameter pipe with com- mercial 5-inch pipe and by the fact that entrance conditions are not the same for the two

methods. Nevertheless the results suggest that we should allow at least a few percent

uncertainty when measuring the partly full condition, since we cannot assess which method

warrants more confidence.

11.4. Trajectory Method (Theoretical)

11.4.1. Background

Treating the water jet as a freely falling body with a constant horizontal velocity

component (equal to the issuing velocity) results in the equation

Q = A(g/2Y)°-^X [11.2]

where Q is the discharge in cfs, A is the sectional area of the issuing water, and X and Y

are trajectory coordinates measured as shown in figure 10.1, except that for this purpose

Y should be referenced to the top of the issuing stream (if this is not the same as the top

inside of the pipe) . Some improvement in results would be obtained if Y could be determined conveniently for the jet centerline, particularly for large X.

11.4.2. General Information Sources

11.4.2.1. "Planning and Making Industrial Waste Surveys," Ohio River Valley Water Sanitation Commission, 414 Walnut Street, Cincinnati, Ohio 45202, 1952, $2.00.

In addition to illustrating the trajectory method, this publication covers other measuring methods -- Parshall flumes, weirs, California Pipe

all in readily readable and understandable fashion, with numerical illustrations .

11.4.3. Comments

As was mentioned in section 11.2.3, the Purdue experimental results do not agree

closely with eq. 11.2. Best overall agreement between the two methods was achieved for

the 2-inch pipe at X = 18 inches, for which the differences were from 4 to 6 percent,

depending on flow. This suggests that the theoretical trajectory computation will give

better results if the measuring station is not too close (in terms of pipe diameters) to the pipe end, and it is recommended that X be taken as large as possible consistent with

the trajectory remaining coherent and parabolic. There is insufficient experimental evidence at present to quantify this recommendation, but there is sufficient evidence to indicate that shorter distances give erroneous results. A point in favor of the theoretical

trajectory method is that adjustments for pipe slope can be made analytically.

11.5. Orifice At End of Pipe

An orifice plate at the end of a pipe, with a trajectory issuing into air, is a simple device often used in irrigation systems. It could have application in certain

industrial waste discharges as well. The setup is shown in figure 11.4, reproduced from

ref. 11.15.1. Also shown are discharge coefficients, C, for use in

Q = CAy2gh [11.3]

where A is the orifice area in square feet, h is the head in feet measured as shown in

figure 11.4, and Q is the flowrate in cubic feet per second (multiply by 449 to obtain

gpm) .

Figure 11.4 also describes how to make an orifice in a standard pipe cap fitting.

78
t

Horizontal ^ ^ d a

> 6d

Figure 11.3. California pipe method, from ref . 11.3.2.1.

1

0.50 0.60 0.70 0.75 0.80

Ratio of orifice to pipe diameter

Figure 11.4. Orifice at end of pipe, from ref. 11.15.1.

79
11.6. Elbow Meters

11.6.1. Background

Centrifugal forces generated in flow around a pipe bend can be measured and used to

determine flowrate. See figure 11.5. Certain commercial pipe elbows can be used (without

in-place calibration) as + 5 percent flowmeters using the procedures and data compiled in

ref. 11.6.2.1.

11.6.2. General Information Sources

11.6.2.1. Replogle, J. A., Myers, L. E. and Brust, K. J., "Evaluation of Pipe Elbows as Flow Meters," Proc . Amer. Soc. Civ. Eng., 92, IR3, Sept. 1966, pp. 17-34. Obtain copy from Engineering Societies Library, 345 E. 47th St., New York, N. Y. 10017. $0.25 per page plus $3.00 handling.

11.6.2.2. "Fluid Meters -- Their Theory and Application," 6th edition, 1971, ASME. Obtain from American Society of Mechanical Engineers, 345 E. 47th St., New York,

N. Y. 10017. $20 ($16 to ASME members).

11.7. Segmental Orifices

11.7.1. Background

A segmental orifice is shown in figure 11.6 and is used mainly for pipe flow which is

heavily debris laden. Segmental orifice coefficients have not been completely characterized with regard to Reynolds number effects. Available information is given in the ref- erence below.

11.7.2. General Information Sources

11.7.2,1. "Fluid Meters," ASME, see ref. 11.6.2.2 for ordering information.

See Chapter II-III, pp. 210-212 for meter coefficients.

11.8. Orifice Meters

11.8.1. Background

This section is concerned with orifice plates within a pipe, as shown in figure 11.7.

This differential head device has long been used, along with the nozzle and Venturi meters

of sections 11.9 and 11.10, for accurate flow measurements. Consequently there is a substantial body of literature on it, including standards and recommended practices, some of

which are cited below.

The basic equation for discharge Q is

Q = CA^(2gh)^^^/(l - P^)^^^ [11.4]

where Aq is the area of the orifice, h is the head difference in height of water between

upstream and downstream taps (which must be located exactly according to recommendations),

P is the orifice-to-pipe diameter ratio, and C is a coefficient which depends upon geometry, Reynolds number and pipe relative roughness. Methods of estimating total tolerance

on Q are given in refs. 11.8.2.2 and 11.8.2.3 below. In order to use standard values

and tolerances for C, the installation conditions cited in the references must be adhered

to strictly.

Because of the large head loss caused by orifice plates, they are not used in pumping

systems where head is an important engineering or economic factor. Also their geometry

makes them unsuitable for some solids-bearing flows, e.g., raw domestic sewage, as is also

the case for thin-plate weirs.

80
n

Figure 11.7. Orifice meter.

81
11.8.2. General Information Sources

"Fluid Meters," ASME, see ref. 11.6.2.2 for ordering information.

Chapter II-II of this book gives complete details on installation and pressure-measurement tubing layouts to minimize errors. Chapter II-III gives

data on flow coefficients.

I. S. 0. Recommendation R541, "Measurement of Fluid Flow by Means of Orifice

Plates and Nozzles," 1967. Order from American National Standards Institute,

1430 Broadway, New York, N. Y. 10018, $15.75.

British Standard 1042: Part 1, "Methods for the Measurement of Fluid Flow in

Pipes, 1. Orifice Plates, Nozzles and Venturi Tubes," 1964. Order from American National Standards Institute, 1430 Broadway, New York, N. Y. 10018.

$13.00.

British Standard 1042: Part 3, "Methods for the Measurement of Fluid Flow in

Pipes, 3. Guide to the Effects of Departure from the Methods in Part 1," 1965.

Order from American National Standards Institute, 1430 Broadway, New York,

N. Y. 10018. $5.40.

References 11.8.2.2 and 11.8.2.3 give detailed information on orifice geometry, installation and coefficients, and are particularly useful in estimating tolerances. Reference 11.8.2.4 gives information only on orifices

and nozzles and not on Venturi tubes.

11.8.3. Errors

Published standards and recommendations give values for the meter coefficient C based

on geometry, pipe size and roughness, and Rejmolds number and attempt to assign tolerances

for "standard" conditions and departures therefrom. The uncertainty of these published

coefficients for standard installations is generally considered to be as high as 2 percent

(e.g., ref. 11.8.2.1). However, errors in the differential head measurement can also con- tribute significantly to the system error. The user must estimate these on his own. It

should be noted as a cautionary example, that a chart recorder (for head) which has an advertised accuracy of 0.5 percent full scale , can show a 5 percent error at 1/lOth capacity. Therefore, it is important to try to design the measurement systems so that all

components will operate as close as possible to rated capacity.

11.9. Nozzle Meters

A nozzle meter is illustrated in figure 10.8. Use the same general information

sources as cited for orifice meters in section 10.8.

11.10. Venturi Meters

11.10.1. Background

Venturi meters have the advantage of reduced head loss relative to orifice and nozzle

meters as well as capability for self cleansing. See figure 11.9. The basic equation is

the same form as eq. 11.4, but with A now referring to the throat area. The coefficient

C is a function of geometry, Reynolds number, roughness and installation conditions.

11.10.2. General Information Sources

11.10.2.1. I. S. 0. Recommendation R781, "Measurement of Fluid Flow by Means of Venturi

Tubes," 1968; and Appendix to R781, "Classical Venturi Tubes Used Outside the

Scope Covered by I. S. 0. Recommendation R781," 1969. Order from American

National Standards Institute, 1430 Broadway, New York, N. Y. 10018. $14.70.

11.8.2.1.

11.8.2.2.

11.8.2.3.

11.8.2.4.

82
11.10.2.2. ASTM Standard D2458-69, "Standard Method of Flow Measurement of Water by the

Venturi Meter Tube." American Society for Testing and Materials, 1916 Race

Street, Philadelphia, Pa. 19103. $1.50.

11.10.2.3. "Fluid Meters," ASME. See ref. 11.6.2.2 for ordering information.

Chapter II-II is a good source for details on pipe layouts, pressure taps

and pressure tubing layout, etc. See chapter III-III for meter coefficients.

11.10.2.4. See also ref. 11.8.2.3.

11.10.3. Errors

The uncertainty in published coefficients for "standard" meter and installation con- ditions ranges up to about 1.5 percent (e.g., ref. 11.8.2.1). See also orifice meter com- ments in section 10.8.3.

11.11. Magnetic Flow Meters

11.11.1. Background

The magnetic flowmeter operates on the same principle as an electric generator, i.e.,

an electromotive force is induced in a conductor. In this case the conductor is the flowing water, and insulated electrodes in the pipe (in a diametric plane normal to the magnetic field) in conjunction with a voltmeter measure the induced emf. Obvious advantages

of this meter are (1) it is nonintrusive and can therefore be used in raw sewage, and (2)

there is no added head loss. A disadvantage is its relatively high cost. The effect of

variation in water conductivity is minimal provided there is a certain threshold conductivity. Velocity-distribution effects are still uncertain and caution should be observed in

that regard.

Build-up of deposit or scale can be an error source depending upon the conductivity of

the deposit. Regular cleaning is necessary. See ref. 11.15.2 for discussion of electrode

maintenance

.

Accuracies of the combined f lowmeter-receiver systems depend upon the components

selected and the method of calibration, but are generally within about 1 percent of full

scale. To this date no standards or recommended practices have been published for this

meter

.

11.11.2. General Information Source

11.11.2.1. "Fluid Meters," ASME, see ref. 11.6.2.2 for ordering information.

See Chapter I-O of this reference, pp. 125-128; see also p. 255.

11.12o Acoustic Flowmeters

11.12.1. Background

Acoustic flowmeters usually employ the difference in transit time of upstream and

downstream directed sonic pulses, this difference being caused by the velocity of the

water in the conduit. See figure 11.10. Various manufacturers employ different electronic methods to take advantage of this principle. Another approach is to measure point

velocities using the acoustic Doppler principle and to convert these to flow rates.

For the most part, the advantages and disadvantages previously listed for the magnetic flowmeter (section 11.11) prevail also for acoustic meters. Accuracy depends upon

(1) the measurement capability of the electronic circuitry, (2) accuracy of measurement of

sound velocity (in some methods the sound velocity cancels out of the equations), and (3)

the accuracy with which the measured chordal velocities are integrated over the flow

section.

83
Flow

Pressure taps

Figure 11.8. Nozzle meter.

See references for

details

.Pressure taps

Figure 11.9. Venturi meter. Flow ^

See references for

details

V

Transducer A

Transducer B

^ ^tT L/( C + V cose )

'BA= L/( C - V cosb )

t is travel time, L is path length,

C is sound speed

Figure 11.10. Acoustic meter principles.

84
According to manufacturers, at least 1 percent accuracy is obtainable. Information on extended field performance is minimal. No standards or recommended practices have been

promulgated for acoustic meters.

11.12.2. General Information Sources

11.12.2.1. Hastings, C. R. , "The LE Acoustic Flowmeter: An Application to Discharge

Measurement," Jour. New England Water Works Assoc., 84, 2, June 1970, 127-151.

Obtain from New England Water Works Association, 727 Statler Office Bldg.

,

Boston, Mass. 02116. $0.50.

This paper describes the "leading edge" meter, in which the time difference between the upstream and downstream travel of the leading edge

of sonic pulses is measured directly.

11.12.2.2. Genthe, W. K. and Yamamoto, M. , "A New Ultrasonic Flowmeter for Flows in Large

Conduits and Open Channels," Paper 2-10-57, AIP/ASME/ISA/NBS Symposium on Flow,

Pittsburgh, Pa. 1971. This paper will appear in Vol. 1 of the symposium

proceedings. Order from Instrument Society of America, 400 Stanwix St.,

Pittsburgh, Pa. 15222. $40.00 (three- volume proceedings, $110).

This paper describes a meter using the "sing-around" frequency counting

method, i.e., a sound pulse arriving at an upstream transducer triggers

a downstream pulse, etc. The reciprocals of the upstream and downstream

travel times are frequencies and their differences can be measured.

11.12.3. Comments

The foregoing two references describe commercially available meters which use two

different methods of effecting the difference measurement described in the first paragraph

of this section. They were cited partly because they are recent but mainly because they

are available in the open literature. They are not intended to comprise an all-inclusive

list. Readers are reminded that other sonic meters are described in manufacturers' literature .

Acoustic flowmeters are also used in open channel flow, and sometimes another acoustic

channel is added to measure flow depth. Schuster (11.15.3) details some of the problems

encountered in acoustic flowrate measurements in a laboratory open channel.

11.13. Chemical Addition Methods

See chapter 9 for the salt velocity method and for dilution methods.

11.14. Velocity-Area Methods

See chapter 8, particularly section 8.7.

11.15. References

11.15.1. "Measurement of Irrigation Water," Section 15, Chapter 9 of National Engineering

Handbook , Soil Conservation Service, U. S. Dept. of Agriculture, 1962. U. S. Government Printing Office, Wash., D. C. 20402. $0.45.

11.15.2. Grey, S., "Electrodes for Magnetic Flowmeters," Water and Sewage Works, 119 , Reference Number, Aug. 1972, pp. R93-R97.

11.15.3. Schuster, J. C, "Measuring Water Velocity With an Ultrasonic Flowmeter," Bur.

Reclamation, Eng. Res. Center, Rep. REC-ERC-72-32 , Sept. 1972.

85
APPENDIX A

SI Conversion Factors

1 inch = 0.0254 metre

1 foot = 0.3048 metre

1 (U. S. liquid) gallon = 0.003785 metres^ = 3785 centimetres^

-6 3

1 (U. S. liquid) gallon per minute = 63.09 x 10 metres per second

= 63.09 centimetres^ per second

APPENDIX B

Definition of Terms

Aeration

Approach velocity

Blockage

Boundary layer

Control (hydraulic)

Critical flow (or depth)

Displacement thickness

See velocity distribution coefficient .

In the context of this publication, the supplying of air to the underside of water overfalls, e.g., at weirs, to relieve the subatmospheric pressures which would otherwise be developed underneath the nappe.

See velocity of approach .

An effect on the registration of a velocity

measuring instrument due to the presence of

the instrument and its support in a conduit

which is not of sufficient size relative to

that of the instrument and support.

The region of a flowing fluid which experiences the frictional effect of the solid

boundary. In pipe or channel flow far downstream of any entrance effect, the boundary

layer grows to occupy the entire flow. However, in developing flow, such as that over

the crest of a rounded-edge weir (fig. 5.1b),

the boundary layer thickness remains only a fraction of the depth.

In the context of this publication, control

points occur at locations of critical flow.

See critical flow .

In open channels, a condition of maximum flow

for available energy. For the same flowrate,

flows which are faster (and shallower) than

critical are called supercritical, and flows

which are slower (and deeper) than critical

are subcritical. A control point separates

regions of subcritical (upstream) and supercritical (downstream) flow.

The amount by which streamlines are shifted

away from the wall as a result of boundary

layer formation. The displacement thickness

times the velocity outside of the boundary

layer equals the amount by which flowrate is

86
reduced owing to the existence of the boundary

layer

Errors, random

Errors, systematic

Free overfall

Froude number

Hydraulic jump

Hydraulic radius

Jump, hydraulic

Kinetic energy coefficient

Macro scale

Overfall, free

Overfall, submerged

Reynolds number

Scow float

Errors whose effect can be reduced by increasing the number of measurements.

Errors which result in an offset between the

measured and "true" flowrate which cannot be

reduced by repetition of the measurement.

See overfall .

A dimensionless number describing the ratio

between inertial and gravity forces, used in

flow systems (such as open channel structures)

where gravity is the important force. producing

motion. It is defined as F = V/(gL) ^ where

g is the acceleration due to gravity and V and

L are a characteristic velocity and length, re- spectively. In parallel open channel flow, a Froude number (based on depth and average velocity) of 1.0 corresponds to critical flow.

A stationary and often extremely turbulent

"shock" front which usually accompanies the

passage of an open channel flow from an upstream supercritical condition to a downstream

subcritical state.

A geometric parameter used in determining flow

resistance properties of a cross-section, defined as the cross-sectional area of flow divided by the wetted perimeter.

See hydraulic jump .

See velocity distribution coefficient .

See turbulence .

A condition in which water flows over an overfall or brink in such a manner that the flow

is unaffected by conditions downstream of the

brink. "Free" overfalls usually refer to

those in which the falling sheet of water is

surrounded on all sides by atmospheric pressure .

See submerged flow .

A dimensionless number describing the ratio

between inertial and viscous forces in a flow

system, used chiefly (but not exclusively) in

closed conduits. It is defined as R = VLp/y,

where p is liquid density, y is the coefficient of dynamic viscosity, V is an average

velocity and L is a characteristic length, e.g.

,

the diameter in pipe flow.

A depth-measuring float used In the mainstream

flow (rather than in a stilling well) of a weir

or flume. It is often scow-shaped, and is

87
connected to an arm which pivots about an upstream pin above the water surface.

Subcritical flow Open channel flow in which the velocity is

lower and the depth higher than for the critical condition (see critical flow) . The

Froude numbers for subcritical flow are less

than 1.0.

Submerged flow, or overfall A condition in which flow over a brink or weir

is affected by the downstream water level. See

also free overfall.

Supercritical flow Open channel flow in which the velocity is

higher and the depth lower than for the critical condition (see critical flow) . The

Froude numbers for supercritical flow are higher than 1.0. Physically speaking, water

waves cannot propagate upstream against a su- percritical flow; hence, the hydraulic jump,

for example.

Turbulence, macroscale If turbulence is considered to consist of a spectrum of turbulent eddy sizes, the macroscale is the size of the largest eddies in

the flow and is of the same order as the con- duit size.

Turbulence, r.m.s,

Turnout

If one measures at a point the instantaneous

velocities in, say, the direction of flow or x-direction, subtracts from them the timeaverage velocity at that point, squares the

differences and takes the square root of the mean of these squares, the result is the x-com- ponent of the r.m.s. turbulence. The turbulence intensity is obtained by dividing this

figure by the time-average velocity and ex- pressing the result as a percentage.

A structure for diverting water from a main

irrigation canal to a subsidiary canal.

Uniform flow

Velocity distribution coefficient, a

Parallel flow in which velocities are the same from point to point along the conduit at a given time. This can occur only in a uniform

conduit, i.e., a conduit whose cross-section

is constant with length.

A factor larger than unity which is applied to

V^/2g (where V is the average velocity in a section area. A) to give the true velocity

head, thus allowing for non-uniform velocity

distribution.

a = v^dA/V^A

where v is the local velocity over an incremental area dA.

Velocity head v2/2g or aV2/2g

88
Velocity of approach The average velocity in the measuring section

immediately upstream of a weir, flume or differential head measuring device.

I

89

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1. PUBLICATION OR REPORT NO.

Spec. Pub. 421

2. Gov't Accession

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3. Recipient's Accession No.

4. TITLE AND SUBTITLE

A Ciiiide to ^/Tethods and Standards for the K'leasurement

of Water Flow

5. Publication Date May 1975

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Gershon Kulin and Philip R. Compton

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16. ABSTRACT (A 200-worcl or less factual summary almost signilicant information. If document includes a significant

bibliography or literature survey, mention it here.)

Selected information sources on methods and standards for making

measurements of water and wastewater flow in the field are listed

and des-cribed. Both closed conduit and free surface flows are treated,

but emphasis is on open channel flow measurements needed in water

resource engineering and in water pollution control. Instruments and

methods covered include weirs, flumes, current meters (and velocity

traverse methods), dilution techniques, pipe flow instruments, acoustic

meters and others. In addition to summarizing the basic properties of

each instrument or method and referring users to the best available

sources of detailed information on performance and field application,

potential sources of error are described and quantified where possible.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Flow measurement, water; instruments, flow measurement; open channel

flow measurement; pipe flow measurement; standards, flow measurement.

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